jacobcd52/hs_math · Datasets at Hugging Face

text stringlengths 45 10k
65° angle with the ground. The base of the cable is 17 ft from the tower. What is the height of the tower to the nearest foot? 8 feet 15 feet 36 feet 40 feet 70. Which of the following has the same value as sin M? sin N tan M cos N cos M CHALLENGE AND EXTEND Algebra Find the value of x. Then find AB, BC, and AC. Round ...
io to determine which angle PRACTICE AND PROBLEM SOLVING For See Exercises Example 21–26 27–32 33–35 36–37 38 1 2 3 4 5 TEKS TEKS TAKS TAKS Skills Practice p. S18 Application Practice p. S35 of the triangle is ∠A. 21. tan A = 5 _ 12 24. sin A = 5 _ 13 22. tan A = 2.4 25. cos A = 12 _ 13 23. sin A = 12 _ 13 26. cos A = ...
ch as ... trigonometric ratios .... Also G.5.D Objective Solve problems involving angles of elevation and angles of depression. Who uses this? Pilots and air traffic controllers use angles of depression to calculate distances. Vocabulary angle of elevation angle of depression An angle of elevation is the angle formed b...
of elevation to the sun is 60°. What is the height of the building? 54 feet 81 feet 107 feet 161 feet 30. Short Response Jim is rafting down a river that runs through a canyon. He sees a trail marker ahead at the top of the canyon and estimates the angle of elevation from the raft to the marker as 45°. Draw a sketch t...
this cable be, and what angle would it make with the ground? Round the length to the nearest tenth and the angle measure to the nearest degree. THINK AND DISCUSS 1. Tell what additional information, if any, is needed to find BC using the Law of Sines. 2. GET ORGANIZED Copy and complete the graphic organizer. Tell whic...
resents the course a kayaker paddles, the magnitude of the vector is the kayaker’s speed. E X A M P L E 2 Finding the Magnitude of a Vector Draw the vector 〈4, -2〉 on a coordinate plane. Find its magnitude to the nearest tenth. Step 1 Draw the vector on a coordinate plane. Use the origin as the initial point. Then (4, ...
to close the window, but she holds the pole at a 75° angle to the floor. Find the vertical component of the force vector in this case. Round to the nearest tenth. c. Who will have an easier time closing the window, Carla or Taneka? (Hint: Who applies more vertical force?) 43. Probability The numbers 1, 2, 3, and 4 are ...
ates to a point on the unit circle. Let P (x, y) be the point where the terminal side of the angle intersects the unit circle. Since P is in Quadrant II, its x-coordinate is negative, and its y-coordinate is positive. So the coordinates of P are (- √  3 ___ 2 , 1 __ 2 ) . The cosine of 150° is the x-coordinate of P, s...
d the direction to the nearest degree. 576 576 Chapter 8 Right Triangles and Trigonometry �� FOCUS ON SAT MATHEMATICS SUBJECT TESTS Though you can use a calculator on the SAT Mathematics Subject Tests, it may be...
f four concrete cylinders arranged in a �� triangular pattern. The center cylinder contains an elevator, which �� takes visitors on a 68-second ride to the top of the tower. �� Choose one or more strategies to solve each problem. 1. The building’s observation deck, the Lookout, is on the fifty-third f...
ference, and Area �� 9-1 Developing Formulas for Triangles and Quadrilaterals TEKS G.5.A Geometric patterns: use ... geometric patterns to develop algebraic expressions representing geometric properties. Also G.1.B, G.3.C, G.3.E, G.8.C Objectives Develop and apply the formulas for the areas of triangles and speci...
hombus has diagonals 500 yd and 800 yd in length. Find the area in square miles. Conversion Factors Metric 1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm Customary 1 mi = 1760 yd 1 mi = 5280 ft 1 yd = 3 ft 1 ft = 12 in. President James Garfield was a classics professor and a major general in the Union Army. He was assassinate...
Substitute 9x 2 π for A. Divide both sides by π. Take the square root of both sides. Step 2 Use the value of r to find the circumference. C = 2πr C = 2π (3x) Substitute 3x for r. C = 6xπ cm Simplify. 1. Find the area of ⊙A in terms of π in which C = (4x - 6) π m. E X A M P L E 2 Music Application A drum kit contains th...
r 2 = 1 __ 2 π (4. 5 2 ) = 10.125π f t 2 shaded area: 21.6 + 27 + 10.125π ≈ 80.4 ft 2 1. Find the shaded area. Round to the nearest tenth, if necessary. 606 606 Chapter 9 Extending Perimeter, Circumference, and Area ��...
e for you. 2 Count the number of lattice points on the boundary of each figure. Record your answers in the table. 3 Count the number of lattice points in the interior of each figure. Record your answers in the table. Figure Area Number of Lattice Points On Boundary In Interior 2.5 5 1 A B C D E F Try This 1. Make a Con...
raw a polygon with a perimeter of 12 units and an area of 4 un its 2 and a polygon with a perimeter of 12 units and an area of 3 un its 2 . 9- 4 Perimeter and Area in the Coordinate Plane 619 619 �� Independent Practice For See E...
rea is doubled, what happens to the p. 623 side length? 6. A circle has a diameter of 14 ft. If the area is tripled, what happens to the circumference. Business A restaurant has a weekly ad in a local newspaper that is 2 inches wide p. 624 and 4 inches high and costs $36.75 per week. The cost of each ad is based on its...
situations. Vocabulary geometric probability Why learn this? You can use geometric probability to estimate how long you may have to wait to cross a street. (See Example 2.) Remember that in probability, the set of all possible outcomes of an experiment is called the sample space. Any set of outcomes is called an event...
ing? c. What is the probability of scoring higher than five points? d. Write About It In an actual event, why might the probabilities be different from those you calculated in parts a, b, and c? Olympic archers stand 70 m from their targets. From that distance, the target appears about the size of the head of a thumbta...
in which C = 14π yd ■ the area, to the nearest tenth, of a regular 13. the diameter of ⊙K in which A = 64 x 2 π m 2 hexagon with apothem 9 yd By the 30°-60°-90° Triangle Theorem, x = 9 √  3 ____ 3 = 3 √3 . So s = 2x = 6 √  3 , and P = 6 (6 √  3 ) = 36 √  3 . aP = 1 _ A = 1 _ (9) (36 √  3 ) = 162 √  3 ≈ 280.6 yd...
= 2ℓ + 2w or P = 2 (ℓ + w) Circumference circle Area rectangle triangle trapezoid C = 2πr or C = πd A = ℓw or A = bh bh or A = bh or circle A = π r 2 Pi π π ≈ 3.14 or π ≈ 22 _ 7 Item A The circumference of a circle is 48π meters. What is the radius in meters? 6.9 meters 24 meters 12 meters 36 meters 1. Which formula wo...
�� ...
the given object. Assume there are no hidden cubes. Top: Bottom: Front: Back: Left: Right: 1. Draw all six orthographic views of the given object. Assume there are no hidden cubes. 10- 2 Representations of Three-Dimensional Figures 661 661 �� Isometric drawing is a way to show three sides of a ...
try of location: develop and use formulas involving length, slope, and midpoint. Also G.5.A, G.8.C, G.9.D Objectives Apply Euler’s formula to find the number of vertices, edges, and faces of a polyhedron. Develop and apply the distance and midpoint formulas in three dimensions. Vocabulary polyhedron space Why learn thi...
to show that Euler’s formula is true for all prisms. 33. Algebra The base of a pyramid is a polygon with n sides. Write an expression for the number of vertices V, the number of edges E, and the number of faces F in terms of n. Use your results to show that Euler’s formula is true for all pyramids. 34. This problem wil...
360 m 2 S = Ph + 2B = 360 + 2 (54 √  3 ) ≈ 547.1 m 2 P = 6 (6) = 36 m The base area is B = 1 __ aP = 54 √  3 m. 2 1. Find the lateral area and surface area of a cube with edge length 8 cm. The lateral surface of a cylinder is the curved surface that connects the two bases. The axis of a cylinder is the segment with ...
llon of paint costs $25, about how much will it cost to paint the walls of the shed? 43. The lateral area of a right rectangular prism is 144 cm 2 . Its length is three times its width, and its height is twice its width. Find its surface area. SPIRAL REVIEW 44. Rebecca’s car can travel 250 miles on one tank of gas. Reb...
. Give your answers in terms of π. 5. 6. 7. a cone with base area 36π ft 2 and slant height 8 ft Describe the effect of each change on the surface area of the given figure. p. 691 8. The dimensions are cut in half. 9. The dimensions are tripled Find the surface area of each composite figure. p. 692 10. 11. 692 12. Craf...
olume of each cylinder. Give your answers both in terms of π and rounded to the nearest tenth. A V = π r 2h = π (8)2(12) Volume of a cylinder Substitute 8 for r and 12 for h. = 768π cm 3 ≈ 2412.7 cm 3 B a cylinder with a base area of 36π in 2 and a height equal to twice the radius Step 1 Use the base area to find the r...
TEKS G.8.D Congruence and the geometry of size: find surface areas and volumes of ..., pyramids, ..., cones, .... Objectives Learn and apply the formula for the volume of a pyramid. Learn and apply the formula for the volume of a cone. Also G.5.A, G.5.B, G.11.D Who uses this? The builders of the Rainforest Pyramid in ...
d Response Find the height in centimeters of a square pyramid with a volume of 243 cm 3 and a base edge length equal to the height. CHALLENGE AND EXTEND Each cone is inscribed in a regular pyramid with a base edge length of 2 ft and a height of 2 ft. Find the volume of each cone. 46. 47. 48. 49. A regular octahedron ha...
�� Independent Practice For See Exercises Example 13–15 16 17–19 20–21 22–23 1 2 3 4 5 TEKS TEKS TAKS TAKS Skills Practice p. S23 Application Practice p. S37 PRACTICE AND PROBLEM SOLVING Find each measurement. Give your answers in terms of π. 13. the volume of the sphere 14. the volume of t...
__ 4 . Describe the effect on the surface area. 10-5 Surface Area of Pyramids and Cones Find the surface area of each figure. Round to the nearest tenth, if necessary. 5. a regular pentagonal pyramid with base edge length 18 yd and slant height 20 yd 6. a right cone with diameter 30 in. and height 8 in. 7. the composit...
ame given to the intersection of a three-dimensional figure and a plane is ? . ̶̶̶̶ 10-1 Solid Geometry (pp. 654–660) TEKS G.2.B, G.6.A, G.6.B, G.9.D E X A M P L E S ■ Classify the figure. Name the vertices, edges, and bases. pentagonal prism vertices: A, B, C, D, E, F, EXERCISES Classify each figure. Name the vertices...
�� Read each test item and answer the questions that follow. �� Measure carefully and make sure you are using the correct units to measure the figure. Item A The net of a cube is shown below. Use a ruler to measure the dimensions of...
center of the circle D. the point at the center of a circle E. the ratio of a circle’s circumference to its diameter Tables and Charts The table shows the number of students in each grade level at Middletown High School. Find each of the following. 5. the percentage of students who are freshman 6. the percentage of stu...
en = 29,000 _ 5280 ≈ 5.49 mi EC = CD + ED Change ft to mi. Seg. Add. Post. = 4000 + 5.49 = 4005.49 mi Substitute 4000 for CD and 5.49 for ED. EC 2 = EH 2 + CH 2 4005.49 2 = EH 2 + 4000 2 43,950.14 ≈ EH 2 210 mi ≈ EH Look Back Pyth. Thm. Substitute the given values. Subtract 4000 2 from both sides. Take the square root ...
n arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them. Arcs and Their Measure ARC MEASURE DIAGRAM A minor arc is an arc whose points are on or in the interior of a central angle. The measure of a minor arc is equal to the measure of its central...
xt term in each pattern. (Lesson 2-1) 57. 1, 3, 7, 13, 21, … 58. C, E, G, I, K, ... 59. 1, 6, 15, … In the figure, (Lesson 11-1) ̶̶ QP and ̶̶̶ QM are tangent to ⊙N. Find each measure. 60. m∠NMQ 61. MQ Construction Circle Through Three Noncollinear Points    Draw three noncollinear points. Construct m and n, the ⊥ bi...
y pushing their feet along the ground! Today the bicycle is a high-tech machine that can include hydraulic brakes and electronic gear changers. 1. A road race bicycle wheel is 28 inches in diameter. A manufacturer makes metal bicycle stands that are 10 in. tall. How long should a stand be to the nearest tenth in order ...
4006a 30. Given: ∠ABC is inscribed in ⊙X with X in the interior of ∠ABC. Prove: m∠ABC = 1 _ m ⁀ AC 2 (Hint: Draw  BX and use Case 1 of the Inscribed Angle Theorem.) History The Winchester Round Table, probably built in the late thirteenth century, is 18 ft across and weighs 1.25 tons. King Arthur’s Round Table of En...
1_ 2 = 1_ 2 = 48° When a person is farsighted, light rays enter the eye and are focused behind the retina. In the eye shown, light rays converge at R. If m ⁀PS = 60° and m ⁀QT = 14°, what is m∠PRS? (m ⁀PS - m ⁀QT ) m∠PRS = 1_ 2 = 1_ 2 = 1_ 2 (60° - 14° ) (46°) = 23° 4. Two of the six muscles that control eye movement ...
cant segment external secant segment tangent segment Who uses this? Archaeologists use facts about segments in circles to help them understand ancient objects. (See Example 2.) In 1901, divers near the Greek island of Antikythera discovered several fragments of ancient items. Using the mathematics of circles, scientist...
ric structure: make conjectures about … circles … choosing from a variety of approaches such as coordinate …. Also G.1.A, G.4.A, G.5.A Objectives Write equations and graph circles in the coordinate plane. Use the equation and graph of a circle to solve problems. Who uses this? Meteorologists use circles and coordinates...
ismograph measures ground motion during an earthquake. To find the epicenter of an earthquake, scientists take readings in three different locations. Then they draw a circle centered at each location. The radius of each circle is the distance the earthquake is from the seismograph. The intersection of the circles is th...
4 congruent circles . . . . . . . . . . . 747 secant . . . . . . . . . . . . . . . . . . . . . 746 Complete the sentences below with vocabulary words from the list above. 1. A(n) ? is a region bounded by an arc and a chord. ̶̶̶̶ 2. An angle whose vertex is at the center of a circle is called a(n) ? . ̶̶̶̶ 3. The measur...
ach test item and answer the questions that follow. Item A Which point is the center of the circle defined by the equation x 2 + (y - 9) 2 = 81? (9, 9) (-9, -9) (0, 9) (9, 0) Item C A regular hexagon is inscribed in a circle with a radius of 8 inches. What is the length of one arc of the circle intercepted by one side ...
ng similar figures G.11.D Similarity and the geometry of shape* describe the effect on perimeter, area, and volume when one or more dimensions of figure are changed and apply this idea in solving problems ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ * Knowledge and skills are written out completely on pages TX28–TX35. 822 822 Chapter 12 Study ...
ven line. 40. x-axis 41. y-axis 42. Write About It Imagine reflecting all the points in a plane across line ℓ. Which points remain fixed under this transformation? That is, for which points is the image the same as the preimage? Explain. Construction Use the construction of a line perpendicular to a given line through ...
slation of the graph of each function along the given vector. 21. 〈3, 0〉 22. 〈-1, -1〉 23. Probability The point P (3, 2) is translated along one of the following four vectors chosen at random: 〈-3, 0〉, 〈-1, -4〉, 〈3, -2〉, and 〈2, 3〉. Find the probability of each of the following. a. The image of P is in the fourth quadr...
y-coordinate. sin 45° = y _ 106 y = 106 sin 45° ≈ 75.0 sin = opp. _ hyp. Solve for y. The car’s location after 5 seconds is approximately (75.0, 75.0) . 4. The London Eye observation wheel has a radius of 67.5 m and takes 30 minutes to make a complete rotation. A car starts at position (67.5, 0) . Find the coordinates...
point matrix that represents the vertices into matrix [B] on your calculator. 2 Enter the matrix ⎡ ⎣ 0 -1 1 0 ⎤ ⎦ into matrix [A]. Multiply [A] * [B] and use the resulting matrix to graph the image of the triangle. Describe the transformation. Try This ⎡ -1 5. Enter the values ⎢ ⎣ 0 ⎤ 0 into matrix [A]. Multiply [A] * ...
e y-axis. Then its image is rotated 90° about the origin. What are the coordinates of the final image of point A under this composition of transformations? (-1, -2) (-2, 1) (1, 2) (-2, -1) 24. Which composition of transformations maps △ABC into the fourth quadrant? Reflect across the x-axis and then reflect across the ...
ane symmetry, symmetry about an axis, or neither. 20. sphere 21. triangular pyramid 22. torus Draw a triangle with the following number of lines of symmetry. Then classify the triangle. 23. exactly one line of symmetry 24. three lines of symmetry 25. no lines of symmetry Data Analysis The graph shown, called the standa...
135° + 135° + 90° = 360° Determine whether the given regular polygon(s) can be used to form a tessellation. If so, draw the tessellation. 4a. 4b. 12-6 Tessellations 865 865 �� THINK AND DISCUSS 1. Explain how you can identify a frieze pattern that has glide reflection symmetry. 2. Is it possible to tessellate a pl...
ge. 2. Copy the figure and the center of dilation. Draw the dilation of RSTU using center Q and a scale factor of 3. E X A M P L E 3 Art Application An artist is creating a large painting from a photograph by dividing the photograph into squares and dilating each square by a scale factor of 4. If the photograph is 20 c...
Find the equation of the image of line ℓ after a dilation centered at the origin with scale factor 3. SPIRAL REVIEW 52. Jerry has a part-time job waiting tables. He kept records comparing the number of customers served to his total amount of tips for the day. If this trend continues, how many customers would he need to...
) , N (5, 2) , P (3, -2) , Q (0, -2) ; 90° 28. G (-2, 1) , H (-3, -2) , J (-1, -4) ; 180° Study Guide: Review 885 885 �� 12-4 Compositions of Transformations (pp. 848–853) TEKS G.5.C, G.10.A E X A M P L E EXERCISES ■ Draw the result of the composition of isometries. Translate ...
use to answer the question. 12. There are only two pieces of information given in this test item that are important to answering this question. What are they? TAKS Tackler 891 891 �� KEYWORD: MG7 TestPrep CUMULATIVE ASSESSMENT, CHAPTERS 1–12 Multiple Choice 1. Which of the following best represe...
ion, Rounding, and Reasonableness . . . . . . . . . . . . . . . . . . . . . . S52 Classify Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S53 Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S53 Prop...
ven: If a triangle is isosceles, then it has two congruent sides. If a triangle has two congruent angles, then it has two congruent sides. Conjecture: If a triangle is isosceles, then it has two congruent angles. 15. Draw a conclusion from the given information. Given: If the sum of the angles of a polygon is 360°, the...
ractice Lesson Lesson Lesson 6-1 2-5 2-5 Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides. 1. 2. 3. Tell whether each polygon is regular or irregular. Tell whether it is concave or convex. 4. 5. 6. 7. Find the measure of each interior angle of pentagon ABCDE. 8. Find the sum...
e spinner to find the probability of each event. 34. the pointer landing on green 35. the pointer landing on blue or red 36. the pointer not landing on orange 37. the pointer not landing on red or yellow Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundre...
nout Year 1998 1996 Voters 12,530 Presidential elections are held every four years. Elections for senators are held every two years. So in years not divisible by 4, only Senate seats are up for election. The table shows voter turnout for a small town during recent election years. Make a conjecture based on the data. (L...
weeds. What angle should the edging form at the vertices of the garden? (Lesson 6-1) Fishing Use the following information for Exercises 3–5. The hinges for the trays in a tackle box form parallelograms to ensure that the trays stay parallel to the base of the box. In ABCD, AB = 21 in., AE = 9 in., and m∠BCD = 125°. ...
ss by drawing his name in block capital letters using one-point perspective. Draw Eli’s logo. (Lesson 10-2) 4. Recreation Two hot air balloons were launched from the same location. The first balloon is 5 miles north, 9 miles east, and 0.5 mile above the launching point. The second balloon is 9 miles north, 5 miles east...
les? Problem-Solving Handbook S41 S41 12��3��4 Guess and Test For complex problems, you can use clues to make guesses and narrow your choices for the solution. Test whether your guess solves the problem, and then continue guessing until you find the solution. Problem-Solving Strategies Draw a Diagram Make a Model Gue...
ntify these facts and draw conclusions from them. Problem-Solving Strategies Draw a Diagram Make a Model Guess and Test Work Backward Find a Pattern Make a Table Solve a Simpler Problem Use Logical Reasoning Use a Venn Diagram Make an Organized List E X A M P L E Dawn, Chloe, and Tyra finish first through third in a cr...
or $12.95 each. Sales tax is 8.25%. How much money does she need? The problem asks for the amount of money, so an exact answer is needed. PRACTICE Round each number to the given place value. 1. 285,618 to the nearest hundred 2. 9.7 to the nearest unit 3. 49.249 to the nearest tenth 4. 873.59 to the nearest ten Estimate...
me number to both sides of an inequality, and the statement will still be true Subtraction Property of Inequality You can subtract the same number from both sides of an inequality, and the statement will still be true. Multiplication and Division Properties of Inequality (by a positive number) You can multiply or divid...
x. E X A M P L E Use the Quadratic Formula to solve each equation. A 2 x 2 + 3 = 7x 2 x 2 - 7x + 3 = 0 Write the equation in standard form. a = 2, b = -7, c = 3 Find a, b, and c. B x 2 - 4x = -6 1x 2 - 4x + 6 = 0 a = 1, b = -4, c = 6 x = - (-7 ) ± √  (-7 ) 2 - 4 (2 ) (3 ) ___ 2 (2 ) Substitute into the Quadratic...
using the relative error , which is the absolute error divided by the actual value. Relative error has no units. When expressed as a percent, this is the percent error of a measurement. E X A M P L E Find the absolute, relative, and percent errors. The first number is the actual value, and the second is the measured va...
0 A.M. to 12 P.M., 72°F from 12 to 2 P.M., 65°F from 2 to 4 P.M., 54°F from 4 to 6 P.M., and 40°F from 6 to 8 P.M. Displaying Data Two other ways to display data are to use a bar graph and a histogram. A bar graph is used when the data values are disjoint, and the data represent categories that are not directly related...
it is perpendicular to the other line. (⊥ Transv. Thm.; p. 173) Thm. 3-4-3 If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other. (2 lines ⊥ to same line → 2 lines ǁ; p. 173) Thm. 3-5-1 Parallel Lines Theorem In a coordinate plane, two nonvertical lines are parallel if...
Midsegment Thm.; p. 431) Chapter 7 Post. 7-3-1 Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. (AA ∼ Post.; p. 470) Thm. 7-3-2 Side-Side-Side (SSS) Similarity Theorem If the three sides of one triangle are proportional...
13. B, E, A 15. Possible answer: ABC 17. 19. Possible answer: planes  and  21. 23. 25. U 27. U 29. If 2 lines intersect, then they intersect in exactly 1 pt. 31. A 33. A 35. Post. 1-1-3 37. Post. 1-1-2 39. C 41. D n (n - 1) _______ 43. 6 45. 2 twins are 11. 49. no 51. mean: 0.44; median: 0.442; mode: 0.44 47. Mother...
ted 1 unit down and is narrower than the graph of the parent function. 49. T 51. S 53. F 2-5 Check It Out! 1. 1 __ 2 t = -7 (Given); 2 ( 1 __ 2 t) = 2 (-7) (Mult. Prop. of =); t = -14 (Simplify.) 2. C = 5 __ 9 (F - 32) (Given); C = 5 __ 9 (86 - 32) (Subst.); C = 5 __ 9 (54) (Simplify.); C = 30 (Simplify.) 3. ∠ Add. Pos...
∠3 ≅ ∠7. r ǁ s by the Conv. of Alt. Int.  Thm. 3. 1. ∠1 ≅ ∠4 (Given) 2. m∠1 = m∠4 (Def. ≅ ) 3. ∠3 and ∠4 are supp. (Given) 4. m∠3 + m∠4 = 180° (Def. supp. ) 5. m∠3 + m∠1 = 180° (Subst.) 6. m∠2 = m∠3 (Vert.  Thm.) 7. m∠2 + m∠1 = 180° (Subst.) 8. ℓ ǁ m (Conv. of Same-Side Int.  Thm.) 4. 4y - 2 = 4 (8) - 2 = 30°; 3y ...
Rt. ∠ ≅ Thm. ̶̶ ̶̶ AB g. SAS Steps 2, 5, 6 AB ≅ Exercises 1. ∠T 3. It is given ̶̶ ̶̶̶ QP . MQ and that ̶̶̶ MP ≅ Thus △MNP ≅ △MQP by SSS. 5. When x = 4, HI = GH = 3, and ̶̶ ̶̶ IJ = GJ = 5. HJ by the Reflex. HJ ≅ Prop. of ≅. Therefore △GHJ ≅ △IHJ by SSS. 7a. Given b. ∠JKL ≅ ∠MLK c. Reflex. Prop. of ≅ d. SAS Steps 1, 2, ...
mdpt.) ̶̶̶ ̶̶ ̶̶̶ 3. ML ≅ GH ≅ JH , ̶̶ ̶̶̶ KM (Given) 4. GJ ≅ ̶̶̶ ̶̶ KL (Div. Prop. of ≅) 5. GH ≅ ̶̶̶ ̶̶ 6. KJ , ∠G ≅ ∠K (Given) GM ≅ 7. △GMH ≅ △KJL (SAS Steps 5, 6) 8. ∠GMH ≅ ∠KJL (CPCTC) 22. (0, 0) , (r, 0) , (0, s) 23. (0, 0) , (2p, 0) , (2p, p) , (0, p) 24. (0, 0) , (8m, 0) , (8m, 8m) , (0, 8m) 25. Use coords. A (...
cus 5. 7.4 6. 13.4 7. 5.8 8. 52° 9. y = x - 1 10. y - 6 = -0.25 (x - 4) 11. No; to apply the Conv. of the ∠ Bisector Thm., you need to know that ̶̶ ̶̶ CB . 12. Yes; because CP ⊥ ̶̶ ̶̶ ̶̶ CP ⊥ AP ≅ CB , and bisector of ∠ABC by the Conv. of the ∠ Bisector Thm. 13. 42.2 14. 46 15. 57.6 16. 46 17. 18 18. 37° 19. (4, 3) 20....
quad. is a . 32. No; a pair of alt. int.  are ≅, so 1 pair of opp. sides are \|\|. A different pair of opp. sides are ≅. None of the conditions ̶̶ for a  are met. 33. slope of BD FH = 1 __ ̶̶ ̶̶ = slope of BH = ̶̶ DF = -6; both pairs of slope of opp. sides have the same slope, so BDFH is a . 34. 18 35. 39.6 36. 39.6...
1 __ 2 7. 3 __ 2 8. 54 9. 17.5; 30; 17.5; 30 10. y = 21 11. s = 10 12. x = ±6 13. z = 13 or z = -11 14. x = ±8 15. y = 3 or y = -5 16. yes; 5 __ 3 ; JKLM ∼ PQRS 17. yes; 2; △TUV ∼ △WXY 18. 1. JL = 1 __ 3 JN , JK = 1 __ 3 JM (Given) Chapter 8 8-1 Check It Out! 1. △LJK ∼ △JMK ∼ △LMJ 2a. 4 2b. 10 √  3 2c. 6 √  2 3. 27; ...
11. 5 __ 12 13. 0.08 15. 0.79 17. 0.78 19. 0.46 21. 0.62 23. 1 __ 2 25. 3 __ 4 27. 0.5 29. 0.11 31. A 33. 0.84 35. 0.13 37. 0.77 39–41. Possible answers given. 39. The point lies on AC. 41. The point lies in the blue triangle or the green triangle. 43. 1 __ 2 ; it does not matter which regions are shaded because they ...
, 4.5, 6) 19. L ≈ 628.3 yd 2 ; S ≈ 785.4 yd 2 20. L = 100 ft 2 ; S = 150 ft 2 21. L = 126 m 2 ; S ≈ 157.2 m 2 22. L = 160 cm 2 ; S ≈ 215.1 cm 2 23. L = 630 ft 2 ; S = 855 ft 2 24. L = 175π m 2 ; S = 224π m 2 25. L = 150π in 2 ; S = 250π in 2 26. S = 800 ft 2 27. S = 448π m 2 28. V = 1080 ft 3 29. V ≈ 1651.7 cm 3 30. V ...
3, with an ∠ of rotational symmetry of 120°. 47. 2a. yes; 120°; order: 3 2b. yes; 180°; order: 2° 2c. no 3a. line symmetry and rotational symmetry; 72°; order: 49. 51. A 53. C 55. 72 57. x = -4 59. x = 0 61. 7 63. $246.40 65. 5 cm 67. P′ (6, -5) 69. P′ (0,-4) 3b. line symmetry; 51.4°; order: 7 4a. both 4b. neither 12-...
of consecutive angles whose common side is a base of the trapezoid. ángulo base de un trapecio Uno de los dos ángulos consecutivos cuyo lado en común es la base del trapecio. base angle of an isosceles triangle (p. 273) One of the two angles that have the base of the triangle as a side. ángulo base de un triángulo isós...
indica que dos polígonos son congruentes enumerando los vértices en orden de correspondencia. congruence transformation (p. 824) See isometry. transformación de congruencia Ver isometría. congruent (p. 13) Having the same size and shape, denoted by ≅. congruente Que tiene el mismo tamaño y forma, expresado por ≅. S122 ...
. diámetro Segmento que atraviesa el centro de un círculo y cuyos extremos están sobre el círculo; longitud de dicho segmento. dilation (p. 495) A transformation in which the lines connecting every point P with its preimage P′ all intersect at a point C known as the center of dilation, and CP′ ___ CP is the same for ev...
S130 Glossary/Glosario a x _ _ = x b x 2 = ab x = √  ab The probability of the pointer landing on red is 2 __ . 9 ��...
tiene puntos espaciados uniformemente en un patrón triangular que se repite. isometry (p. 824) A transformation that does not change the size or shape of a figure. isosceles trapezoid (p. 429) A trapezoid in which the legs are congruent. isometría Transformación que no cambia el tamaño ni la forma de una figura. Refle...
lateral face. prisma oblicuo Prisma que tiene por lo menos una cara lateral no rectangular. obtuse angle (p. 21) An angle that measures greater than 90° and less than 180°. ángulo obtuso Ángulo que mide más de 90° y menos de 180°. obtuse triangle (p. 216) A triangle with one obtuse angle. triángulo obtusángulo Triángul...
ch distances are measured in a polar coordinate system. SPANISH polo Punto desde el que se miden las distancias en un sistema de coordenadas polares. EXAMPLES polygon (p. 98) A closed plane figure formed by three or more segments such that each segment intersects exactly two other segments only at their endpoints and n...
t. rotación Transformación sobre un punto P, también conocido como el centro de rotación, tal que cada punto y su imagen estén a la misma distancia de P. Todos los ángulos con vértice P formados por un punto y su imagen son congruentes. rotational symmetry (p. 857) A figure that can be rotated about a point by an angle...
° triangle or a 30°-60°-90° triangle. triángulo rectángulo especial Triángulo de 45°-45°-90° o triángulo de 30°-60°-90°. y = -2x + 4 The slope is -2. The y-intercept is 4. Glossary/Glosario S153 S153 �� ENGLISH sphere (p. 714) The set of points in space that ...
ectiva de dos puntos Dibujo en perspectiva con dos puntos de fuga. U undefined term (p. 6) A basic figure that is not defined in terms of other figures. The undefined terms in geometry are point, line, and plane. término indefinido Figura básica que no está definida en función de otras figuras. Los términos indefinidos...
kythera, 792 Antique speakers, 692 Apothem, 601 Applications Advertising, 499 Agriculture, 765 Animation, 53, 835, 842 Anthropology, 802 Archaeology, 262, 787, 793 Architecture, 47, 159, 166, 220, 324, 457, 467, 485, 529, 658, 667, 695, 706, 767, 843, 859, 875 Art, 10, 32, 167, 465, 483, 557, 593, 657, 668, 834, 849, 8...
, 185, 193, 218, 226, 245, 255, 262, 269, 276, 303, 310, 324, 335, 342, 352, 359, 385, 421, 431, 457, 473, 490, 497, 520, 546, 563, 593, 602, 608, 619, 633, 673, 683, 692, 700, 708, 717, 750, 766, 775, 786, 801, 826, 833, 850, 858, 866, 874 justify, 394, 801 list, 113, 148, 352 name, 8, 24, 218, 233, 593 sketch (draw),...
76, 880 Estimating area under curves, 621 Estimation, 25, 37, 41, 77, 108, 177, 195, 229, 278, 325, 361, 387, 433, 466, 492, 493, 538, 565, 611, 621, 676, 719, 768, 803, 844, 877, S52 rounding and, S52 Estimation strategies, 578–579 Euclid, 257, 460 Euler, Leonhard, 78 Euler line, 321 Euler’s Formula, 670 Event, 628 co...
tion, 278 Recreation, 92 Shuffleboard, 305 Sports, 19, 635 Surveying, 353, 556 Travel, 458 Literal equations, 41, 169, 588, 590 Locus, 300, 302, 304, 306, 600, 714, 743, 804 Logic puzzles, solving, 94–95 Logically equivalent statements, 83 Lune, 611 Lunette, 767 Luxor Hotel, 159 M Madurodam, 458 Magnitude of a vector, ...

65° angle with the ground. The base of the cable is 17 ft from the tower. What is the height of the tower to the nearest foot? 8 feet 15 feet 36 feet 40 feet 70. Which of the following has the same value as sin M? sin N tan M cos N cos M CHALLENGE AND EXTEND Algebra Find the value of x. Then find AB, BC, and AC. Round ...

io to determine which angle PRACTICE AND PROBLEM SOLVING For See Exercises Example 21–26 27–32 33–35 36–37 38 1 2 3 4 5 TEKS TEKS TAKS TAKS Skills Practice p. S18 Application Practice p. S35 of the triangle is ∠A. 21. tan A = 5 _ 12 24. sin A = 5 _ 13 22. tan A = 2.4 25. cos A = 12 _ 13 23. sin A = 12 _ 13 26. cos A = ...

ch as ... trigonometric ratios .... Also G.5.D Objective Solve problems involving angles of elevation and angles of depression. Who uses this? Pilots and air traffic controllers use angles of depression to calculate distances. Vocabulary angle of elevation angle of depression An angle of elevation is the angle formed b...

of elevation to the sun is 60°. What is the height of the building? 54 feet 81 feet 107 feet 161 feet 30. Short Response Jim is rafting down a river that runs through a canyon. He sees a trail marker ahead at the top of the canyon and estimates the angle of elevation from the raft to the marker as 45°. Draw a sketch t...

this cable be, and what angle would it make with the ground? Round the length to the nearest tenth and the angle measure to the nearest degree. THINK AND DISCUSS 1. Tell what additional information, if any, is needed to find BC using the Law of Sines. 2. GET ORGANIZED Copy and complete the graphic organizer. Tell whic...

resents the course a kayaker paddles, the magnitude of the vector is the kayaker’s speed. E X A M P L E 2 Finding the Magnitude of a Vector Draw the vector 〈4, -2〉 on a coordinate plane. Find its magnitude to the nearest tenth. Step 1 Draw the vector on a coordinate plane. Use the origin as the initial point. Then (4, ...

to close the window, but she holds the pole at a 75° angle to the floor. Find the vertical component of the force vector in this case. Round to the nearest tenth. c. Who will have an easier time closing the window, Carla or Taneka? (Hint: Who applies more vertical force?) 43. Probability The numbers 1, 2, 3, and 4 are ...

ates to a point on the unit circle. Let P (x, y) be the point where the terminal side of the angle intersects the unit circle. Since P is in Quadrant II, its x-coordinate is negative, and its y-coordinate is positive. So the coordinates of P are (- √  3 ___ 2 , 1 __ 2 ) . The cosine of 150° is the x-coordinate of P, s...

d the direction to the nearest degree. 576 576 Chapter 8 Right Triangles and Trigonometry �� FOCUS ON SAT MATHEMATICS SUBJECT TESTS Though you can use a calculator on the SAT Mathematics Subject Tests, it may be...

f four concrete cylinders arranged in a �� triangular pattern. The center cylinder contains an elevator, which �� takes visitors on a 68-second ride to the top of the tower. �� Choose one or more strategies to solve each problem. 1. The building’s observation deck, the Lookout, is on the fifty-third f...

ference, and Area �� 9-1 Developing Formulas for Triangles and Quadrilaterals TEKS G.5.A Geometric patterns: use ... geometric patterns to develop algebraic expressions representing geometric properties. Also G.1.B, G.3.C, G.3.E, G.8.C Objectives Develop and apply the formulas for the areas of triangles and speci...

hombus has diagonals 500 yd and 800 yd in length. Find the area in square miles. Conversion Factors Metric 1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm Customary 1 mi = 1760 yd 1 mi = 5280 ft 1 yd = 3 ft 1 ft = 12 in. President James Garfield was a classics professor and a major general in the Union Army. He was assassinate...

Substitute 9x 2 π for A. Divide both sides by π. Take the square root of both sides. Step 2 Use the value of r to find the circumference. C = 2πr C = 2π (3x) Substitute 3x for r. C = 6xπ cm Simplify. 1. Find the area of ⊙A in terms of π in which C = (4x - 6) π m. E X A M P L E 2 Music Application A drum kit contains th...

r 2 = 1 __ 2 π (4. 5 2 ) = 10.125π f t 2 shaded area: 21.6 + 27 + 10.125π ≈ 80.4 ft 2 1. Find the shaded area. Round to the nearest tenth, if necessary. 606 606 Chapter 9 Extending Perimeter, Circumference, and Area ��...

e for you. 2 Count the number of lattice points on the boundary of each figure. Record your answers in the table. 3 Count the number of lattice points in the interior of each figure. Record your answers in the table. Figure Area Number of Lattice Points On Boundary In Interior 2.5 5 1 A B C D E F Try This 1. Make a Con...

raw a polygon with a perimeter of 12 units and an area of 4 un its 2 and a polygon with a perimeter of 12 units and an area of 3 un its 2 . 9- 4 Perimeter and Area in the Coordinate Plane 619 619 �� Independent Practice For See E...

rea is doubled, what happens to the p. 623 side length? 6. A circle has a diameter of 14 ft. If the area is tripled, what happens to the circumference. Business A restaurant has a weekly ad in a local newspaper that is 2 inches wide p. 624 and 4 inches high and costs $36.75 per week. The cost of each ad is based on its...

situations. Vocabulary geometric probability Why learn this? You can use geometric probability to estimate how long you may have to wait to cross a street. (See Example 2.) Remember that in probability, the set of all possible outcomes of an experiment is called the sample space. Any set of outcomes is called an event...

ing? c. What is the probability of scoring higher than five points? d. Write About It In an actual event, why might the probabilities be different from those you calculated in parts a, b, and c? Olympic archers stand 70 m from their targets. From that distance, the target appears about the size of the head of a thumbta...

in which C = 14π yd ■ the area, to the nearest tenth, of a regular 13. the diameter of ⊙K in which A = 64 x 2 π m 2 hexagon with apothem 9 yd By the 30°-60°-90° Triangle Theorem, x = 9 √  3 ____ 3 = 3 √3 . So s = 2x = 6 √  3 , and P = 6 (6 √  3 ) = 36 √  3 . aP = 1 _ A = 1 _ (9) (36 √  3 ) = 162 √  3 ≈ 280.6 yd...

= 2ℓ + 2w or P = 2 (ℓ + w) Circumference circle Area rectangle triangle trapezoid C = 2πr or C = πd A = ℓw or A = bh bh or A = bh or circle A = π r 2 Pi π π ≈ 3.14 or π ≈ 22 _ 7 Item A The circumference of a circle is 48π meters. What is the radius in meters? 6.9 meters 24 meters 12 meters 36 meters 1. Which formula wo...

�� ...

the given object. Assume there are no hidden cubes. Top: Bottom: Front: Back: Left: Right: 1. Draw all six orthographic views of the given object. Assume there are no hidden cubes. 10- 2 Representations of Three-Dimensional Figures 661 661 �� Isometric drawing is a way to show three sides of a ...

try of location: develop and use formulas involving length, slope, and midpoint. Also G.5.A, G.8.C, G.9.D Objectives Apply Euler’s formula to find the number of vertices, edges, and faces of a polyhedron. Develop and apply the distance and midpoint formulas in three dimensions. Vocabulary polyhedron space Why learn thi...

to show that Euler’s formula is true for all prisms. 33. Algebra The base of a pyramid is a polygon with n sides. Write an expression for the number of vertices V, the number of edges E, and the number of faces F in terms of n. Use your results to show that Euler’s formula is true for all pyramids. 34. This problem wil...

360 m 2 S = Ph + 2B = 360 + 2 (54 √  3 ) ≈ 547.1 m 2 P = 6 (6) = 36 m The base area is B = 1 __ aP = 54 √  3 m. 2 1. Find the lateral area and surface area of a cube with edge length 8 cm. The lateral surface of a cylinder is the curved surface that connects the two bases. The axis of a cylinder is the segment with ...

llon of paint costs $25, about how much will it cost to paint the walls of the shed? 43. The lateral area of a right rectangular prism is 144 cm 2 . Its length is three times its width, and its height is twice its width. Find its surface area. SPIRAL REVIEW 44. Rebecca’s car can travel 250 miles on one tank of gas. Reb...

. Give your answers in terms of π. 5. 6. 7. a cone with base area 36π ft 2 and slant height 8 ft Describe the effect of each change on the surface area of the given figure. p. 691 8. The dimensions are cut in half. 9. The dimensions are tripled Find the surface area of each composite figure. p. 692 10. 11. 692 12. Craf...

olume of each cylinder. Give your answers both in terms of π and rounded to the nearest tenth. A V = π r 2h = π (8)2(12) Volume of a cylinder Substitute 8 for r and 12 for h. = 768π cm 3 ≈ 2412.7 cm 3 B a cylinder with a base area of 36π in 2 and a height equal to twice the radius Step 1 Use the base area to find the r...

TEKS G.8.D Congruence and the geometry of size: find surface areas and volumes of ..., pyramids, ..., cones, .... Objectives Learn and apply the formula for the volume of a pyramid. Learn and apply the formula for the volume of a cone. Also G.5.A, G.5.B, G.11.D Who uses this? The builders of the Rainforest Pyramid in ...

d Response Find the height in centimeters of a square pyramid with a volume of 243 cm 3 and a base edge length equal to the height. CHALLENGE AND EXTEND Each cone is inscribed in a regular pyramid with a base edge length of 2 ft and a height of 2 ft. Find the volume of each cone. 46. 47. 48. 49. A regular octahedron ha...

�� Independent Practice For See Exercises Example 13–15 16 17–19 20–21 22–23 1 2 3 4 5 TEKS TEKS TAKS TAKS Skills Practice p. S23 Application Practice p. S37 PRACTICE AND PROBLEM SOLVING Find each measurement. Give your answers in terms of π. 13. the volume of the sphere 14. the volume of t...

__ 4 . Describe the effect on the surface area. 10-5 Surface Area of Pyramids and Cones Find the surface area of each figure. Round to the nearest tenth, if necessary. 5. a regular pentagonal pyramid with base edge length 18 yd and slant height 20 yd 6. a right cone with diameter 30 in. and height 8 in. 7. the composit...

ame given to the intersection of a three-dimensional figure and a plane is ? . ̶̶̶̶ 10-1 Solid Geometry (pp. 654–660) TEKS G.2.B, G.6.A, G.6.B, G.9.D E X A M P L E S ■ Classify the figure. Name the vertices, edges, and bases. pentagonal prism vertices: A, B, C, D, E, F, EXERCISES Classify each figure. Name the vertices...

�� Read each test item and answer the questions that follow. �� Measure carefully and make sure you are using the correct units to measure the figure. Item A The net of a cube is shown below. Use a ruler to measure the dimensions of...

center of the circle D. the point at the center of a circle E. the ratio of a circle’s circumference to its diameter Tables and Charts The table shows the number of students in each grade level at Middletown High School. Find each of the following. 5. the percentage of students who are freshman 6. the percentage of stu...

en = 29,000 _ 5280 ≈ 5.49 mi EC = CD + ED Change ft to mi. Seg. Add. Post. = 4000 + 5.49 = 4005.49 mi Substitute 4000 for CD and 5.49 for ED. EC 2 = EH 2 + CH 2 4005.49 2 = EH 2 + 4000 2 43,950.14 ≈ EH 2 210 mi ≈ EH Look Back Pyth. Thm. Substitute the given values. Subtract 4000 2 from both sides. Take the square root ...

n arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them. Arcs and Their Measure ARC MEASURE DIAGRAM A minor arc is an arc whose points are on or in the interior of a central angle. The measure of a minor arc is equal to the measure of its central...

xt term in each pattern. (Lesson 2-1) 57. 1, 3, 7, 13, 21, … 58. C, E, G, I, K, ... 59. 1, 6, 15, … In the figure, (Lesson 11-1) ̶̶ QP and ̶̶̶ QM are tangent to ⊙N. Find each measure. 60. m∠NMQ 61. MQ Construction Circle Through Three Noncollinear Points    Draw three noncollinear points. Construct m and n, the ⊥ bi...

y pushing their feet along the ground! Today the bicycle is a high-tech machine that can include hydraulic brakes and electronic gear changers. 1. A road race bicycle wheel is 28 inches in diameter. A manufacturer makes metal bicycle stands that are 10 in. tall. How long should a stand be to the nearest tenth in order ...

4006a 30. Given: ∠ABC is inscribed in ⊙X with X in the interior of ∠ABC. Prove: m∠ABC = 1 _ m ⁀ AC 2 (Hint: Draw  BX and use Case 1 of the Inscribed Angle Theorem.) History The Winchester Round Table, probably built in the late thirteenth century, is 18 ft across and weighs 1.25 tons. King Arthur’s Round Table of En...

1_ 2 = 1_ 2 = 48° When a person is farsighted, light rays enter the eye and are focused behind the retina. In the eye shown, light rays converge at R. If m ⁀PS = 60° and m ⁀QT = 14°, what is m∠PRS? (m ⁀PS - m ⁀QT ) m∠PRS = 1_ 2 = 1_ 2 = 1_ 2 (60° - 14° ) (46°) = 23° 4. Two of the six muscles that control eye movement ...

cant segment external secant segment tangent segment Who uses this? Archaeologists use facts about segments in circles to help them understand ancient objects. (See Example 2.) In 1901, divers near the Greek island of Antikythera discovered several fragments of ancient items. Using the mathematics of circles, scientist...

ric structure: make conjectures about … circles … choosing from a variety of approaches such as coordinate …. Also G.1.A, G.4.A, G.5.A Objectives Write equations and graph circles in the coordinate plane. Use the equation and graph of a circle to solve problems. Who uses this? Meteorologists use circles and coordinates...

ismograph measures ground motion during an earthquake. To find the epicenter of an earthquake, scientists take readings in three different locations. Then they draw a circle centered at each location. The radius of each circle is the distance the earthquake is from the seismograph. The intersection of the circles is th...

4 congruent circles . . . . . . . . . . . 747 secant . . . . . . . . . . . . . . . . . . . . . 746 Complete the sentences below with vocabulary words from the list above. 1. A(n) ? is a region bounded by an arc and a chord. ̶̶̶̶ 2. An angle whose vertex is at the center of a circle is called a(n) ? . ̶̶̶̶ 3. The measur...

ach test item and answer the questions that follow. Item A Which point is the center of the circle defined by the equation x 2 + (y - 9) 2 = 81? (9, 9) (-9, -9) (0, 9) (9, 0) Item C A regular hexagon is inscribed in a circle with a radius of 8 inches. What is the length of one arc of the circle intercepted by one side ...

ng similar figures G.11.D Similarity and the geometry of shape* describe the effect on perimeter, area, and volume when one or more dimensions of figure are changed and apply this idea in solving problems ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ * Knowledge and skills are written out completely on pages TX28–TX35. 822 822 Chapter 12 Study ...

ven line. 40. x-axis 41. y-axis 42. Write About It Imagine reflecting all the points in a plane across line ℓ. Which points remain fixed under this transformation? That is, for which points is the image the same as the preimage? Explain. Construction Use the construction of a line perpendicular to a given line through ...

slation of the graph of each function along the given vector. 21. 〈3, 0〉 22. 〈-1, -1〉 23. Probability The point P (3, 2) is translated along one of the following four vectors chosen at random: 〈-3, 0〉, 〈-1, -4〉, 〈3, -2〉, and 〈2, 3〉. Find the probability of each of the following. a. The image of P is in the fourth quadr...

y-coordinate. sin 45° = y _ 106 y = 106 sin 45° ≈ 75.0 sin = opp. _ hyp. Solve for y. The car’s location after 5 seconds is approximately (75.0, 75.0) . 4. The London Eye observation wheel has a radius of 67.5 m and takes 30 minutes to make a complete rotation. A car starts at position (67.5, 0) . Find the coordinates...

point matrix that represents the vertices into matrix [B] on your calculator. 2 Enter the matrix ⎡ ⎣ 0 -1 1 0 ⎤ ⎦ into matrix [A]. Multiply [A] * [B] and use the resulting matrix to graph the image of the triangle. Describe the transformation. Try This ⎡ -1 5. Enter the values ⎢ ⎣ 0 ⎤ 0 into matrix [A]. Multiply [A] * ...

e y-axis. Then its image is rotated 90° about the origin. What are the coordinates of the final image of point A under this composition of transformations? (-1, -2) (-2, 1) (1, 2) (-2, -1) 24. Which composition of transformations maps △ABC into the fourth quadrant? Reflect across the x-axis and then reflect across the ...

ane symmetry, symmetry about an axis, or neither. 20. sphere 21. triangular pyramid 22. torus Draw a triangle with the following number of lines of symmetry. Then classify the triangle. 23. exactly one line of symmetry 24. three lines of symmetry 25. no lines of symmetry Data Analysis The graph shown, called the standa...

135° + 135° + 90° = 360° Determine whether the given regular polygon(s) can be used to form a tessellation. If so, draw the tessellation. 4a. 4b. 12-6 Tessellations 865 865 �� THINK AND DISCUSS 1. Explain how you can identify a frieze pattern that has glide reflection symmetry. 2. Is it possible to tessellate a pl...

ge. 2. Copy the figure and the center of dilation. Draw the dilation of RSTU using center Q and a scale factor of 3. E X A M P L E 3 Art Application An artist is creating a large painting from a photograph by dividing the photograph into squares and dilating each square by a scale factor of 4. If the photograph is 20 c...

Find the equation of the image of line ℓ after a dilation centered at the origin with scale factor 3. SPIRAL REVIEW 52. Jerry has a part-time job waiting tables. He kept records comparing the number of customers served to his total amount of tips for the day. If this trend continues, how many customers would he need to...

) , N (5, 2) , P (3, -2) , Q (0, -2) ; 90° 28. G (-2, 1) , H (-3, -2) , J (-1, -4) ; 180° Study Guide: Review 885 885 �� 12-4 Compositions of Transformations (pp. 848–853) TEKS G.5.C, G.10.A E X A M P L E EXERCISES ■ Draw the result of the composition of isometries. Translate ...

use to answer the question. 12. There are only two pieces of information given in this test item that are important to answering this question. What are they? TAKS Tackler 891 891 �� KEYWORD: MG7 TestPrep CUMULATIVE ASSESSMENT, CHAPTERS 1–12 Multiple Choice 1. Which of the following best represe...

ion, Rounding, and Reasonableness . . . . . . . . . . . . . . . . . . . . . . S52 Classify Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S53 Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S53 Prop...

ven: If a triangle is isosceles, then it has two congruent sides. If a triangle has two congruent angles, then it has two congruent sides. Conjecture: If a triangle is isosceles, then it has two congruent angles. 15. Draw a conclusion from the given information. Given: If the sum of the angles of a polygon is 360°, the...

ractice Lesson Lesson Lesson 6-1 2-5 2-5 Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides. 1. 2. 3. Tell whether each polygon is regular or irregular. Tell whether it is concave or convex. 4. 5. 6. 7. Find the measure of each interior angle of pentagon ABCDE. 8. Find the sum...

e spinner to find the probability of each event. 34. the pointer landing on green 35. the pointer landing on blue or red 36. the pointer not landing on orange 37. the pointer not landing on red or yellow Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundre...

nout Year 1998 1996 Voters 12,530 Presidential elections are held every four years. Elections for senators are held every two years. So in years not divisible by 4, only Senate seats are up for election. The table shows voter turnout for a small town during recent election years. Make a conjecture based on the data. (L...

weeds. What angle should the edging form at the vertices of the garden? (Lesson 6-1) Fishing Use the following information for Exercises 3–5. The hinges for the trays in a tackle box form parallelograms to ensure that the trays stay parallel to the base of the box. In ABCD, AB = 21 in., AE = 9 in., and m∠BCD = 125°. ...

ss by drawing his name in block capital letters using one-point perspective. Draw Eli’s logo. (Lesson 10-2) 4. Recreation Two hot air balloons were launched from the same location. The first balloon is 5 miles north, 9 miles east, and 0.5 mile above the launching point. The second balloon is 9 miles north, 5 miles east...

les? Problem-Solving Handbook S41 S41 12��3��4 Guess and Test For complex problems, you can use clues to make guesses and narrow your choices for the solution. Test whether your guess solves the problem, and then continue guessing until you find the solution. Problem-Solving Strategies Draw a Diagram Make a Model Gue...

ntify these facts and draw conclusions from them. Problem-Solving Strategies Draw a Diagram Make a Model Guess and Test Work Backward Find a Pattern Make a Table Solve a Simpler Problem Use Logical Reasoning Use a Venn Diagram Make an Organized List E X A M P L E Dawn, Chloe, and Tyra finish first through third in a cr...

or $12.95 each. Sales tax is 8.25%. How much money does she need? The problem asks for the amount of money, so an exact answer is needed. PRACTICE Round each number to the given place value. 1. 285,618 to the nearest hundred 2. 9.7 to the nearest unit 3. 49.249 to the nearest tenth 4. 873.59 to the nearest ten Estimate...

me number to both sides of an inequality, and the statement will still be true Subtraction Property of Inequality You can subtract the same number from both sides of an inequality, and the statement will still be true. Multiplication and Division Properties of Inequality (by a positive number) You can multiply or divid...

x. E X A M P L E Use the Quadratic Formula to solve each equation. A 2 x 2 + 3 = 7x 2 x 2 - 7x + 3 = 0 Write the equation in standard form. a = 2, b = -7, c = 3 Find a, b, and c. B x 2 - 4x = -6 1x 2 - 4x + 6 = 0 a = 1, b = -4, c = 6 x = - (-7 ) ± √  (-7 ) 2 - 4 (2 ) (3 ) ___ 2 (2 ) Substitute into the Quadratic...

using the relative error , which is the absolute error divided by the actual value. Relative error has no units. When expressed as a percent, this is the percent error of a measurement. E X A M P L E Find the absolute, relative, and percent errors. The first number is the actual value, and the second is the measured va...

0 A.M. to 12 P.M., 72°F from 12 to 2 P.M., 65°F from 2 to 4 P.M., 54°F from 4 to 6 P.M., and 40°F from 6 to 8 P.M. Displaying Data Two other ways to display data are to use a bar graph and a histogram. A bar graph is used when the data values are disjoint, and the data represent categories that are not directly related...

it is perpendicular to the other line. (⊥ Transv. Thm.; p. 173) Thm. 3-4-3 If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other. (2 lines ⊥ to same line → 2 lines ǁ; p. 173) Thm. 3-5-1 Parallel Lines Theorem In a coordinate plane, two nonvertical lines are parallel if...

Midsegment Thm.; p. 431) Chapter 7 Post. 7-3-1 Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. (AA ∼ Post.; p. 470) Thm. 7-3-2 Side-Side-Side (SSS) Similarity Theorem If the three sides of one triangle are proportional...

13. B, E, A 15. Possible answer: ABC 17. 19. Possible answer: planes  and  21. 23. 25. U 27. U 29. If 2 lines intersect, then they intersect in exactly 1 pt. 31. A 33. A 35. Post. 1-1-3 37. Post. 1-1-2 39. C 41. D n (n - 1) _______ 43. 6 45. 2 twins are 11. 49. no 51. mean: 0.44; median: 0.442; mode: 0.44 47. Mother...

ted 1 unit down and is narrower than the graph of the parent function. 49. T 51. S 53. F 2-5 Check It Out! 1. 1 __ 2 t = -7 (Given); 2 ( 1 __ 2 t) = 2 (-7) (Mult. Prop. of =); t = -14 (Simplify.) 2. C = 5 __ 9 (F - 32) (Given); C = 5 __ 9 (86 - 32) (Subst.); C = 5 __ 9 (54) (Simplify.); C = 30 (Simplify.) 3. ∠ Add. Pos...

∠3 ≅ ∠7. r ǁ s by the Conv. of Alt. Int.  Thm. 3. 1. ∠1 ≅ ∠4 (Given) 2. m∠1 = m∠4 (Def. ≅ ) 3. ∠3 and ∠4 are supp. (Given) 4. m∠3 + m∠4 = 180° (Def. supp. ) 5. m∠3 + m∠1 = 180° (Subst.) 6. m∠2 = m∠3 (Vert.  Thm.) 7. m∠2 + m∠1 = 180° (Subst.) 8. ℓ ǁ m (Conv. of Same-Side Int.  Thm.) 4. 4y - 2 = 4 (8) - 2 = 30°; 3y ...

Rt. ∠ ≅ Thm. ̶̶ ̶̶ AB g. SAS Steps 2, 5, 6 AB ≅ Exercises 1. ∠T 3. It is given ̶̶ ̶̶̶ QP . MQ and that ̶̶̶ MP ≅ Thus △MNP ≅ △MQP by SSS. 5. When x = 4, HI = GH = 3, and ̶̶ ̶̶ IJ = GJ = 5. HJ by the Reflex. HJ ≅ Prop. of ≅. Therefore △GHJ ≅ △IHJ by SSS. 7a. Given b. ∠JKL ≅ ∠MLK c. Reflex. Prop. of ≅ d. SAS Steps 1, 2, ...

mdpt.) ̶̶̶ ̶̶ ̶̶̶ 3. ML ≅ GH ≅ JH , ̶̶ ̶̶̶ KM (Given) 4. GJ ≅ ̶̶̶ ̶̶ KL (Div. Prop. of ≅) 5. GH ≅ ̶̶̶ ̶̶ 6. KJ , ∠G ≅ ∠K (Given) GM ≅ 7. △GMH ≅ △KJL (SAS Steps 5, 6) 8. ∠GMH ≅ ∠KJL (CPCTC) 22. (0, 0) , (r, 0) , (0, s) 23. (0, 0) , (2p, 0) , (2p, p) , (0, p) 24. (0, 0) , (8m, 0) , (8m, 8m) , (0, 8m) 25. Use coords. A (...

cus 5. 7.4 6. 13.4 7. 5.8 8. 52° 9. y = x - 1 10. y - 6 = -0.25 (x - 4) 11. No; to apply the Conv. of the ∠ Bisector Thm., you need to know that ̶̶ ̶̶ CB . 12. Yes; because CP ⊥ ̶̶ ̶̶ ̶̶ CP ⊥ AP ≅ CB , and bisector of ∠ABC by the Conv. of the ∠ Bisector Thm. 13. 42.2 14. 46 15. 57.6 16. 46 17. 18 18. 37° 19. (4, 3) 20....

quad. is a . 32. No; a pair of alt. int.  are ≅, so 1 pair of opp. sides are ||. A different pair of opp. sides are ≅. None of the conditions ̶̶ for a  are met. 33. slope of BD FH = 1 __ ̶̶ ̶̶ = slope of BH = ̶̶ DF = -6; both pairs of slope of opp. sides have the same slope, so BDFH is a . 34. 18 35. 39.6 36. 39.6...

1 __ 2 7. 3 __ 2 8. 54 9. 17.5; 30; 17.5; 30 10. y = 21 11. s = 10 12. x = ±6 13. z = 13 or z = -11 14. x = ±8 15. y = 3 or y = -5 16. yes; 5 __ 3 ; JKLM ∼ PQRS 17. yes; 2; △TUV ∼ △WXY 18. 1. JL = 1 __ 3 JN , JK = 1 __ 3 JM (Given) Chapter 8 8-1 Check It Out! 1. △LJK ∼ △JMK ∼ △LMJ 2a. 4 2b. 10 √  3 2c. 6 √  2 3. 27; ...

11. 5 __ 12 13. 0.08 15. 0.79 17. 0.78 19. 0.46 21. 0.62 23. 1 __ 2 25. 3 __ 4 27. 0.5 29. 0.11 31. A 33. 0.84 35. 0.13 37. 0.77 39–41. Possible answers given. 39. The point lies on AC. 41. The point lies in the blue triangle or the green triangle. 43. 1 __ 2 ; it does not matter which regions are shaded because they ...

, 4.5, 6) 19. L ≈ 628.3 yd 2 ; S ≈ 785.4 yd 2 20. L = 100 ft 2 ; S = 150 ft 2 21. L = 126 m 2 ; S ≈ 157.2 m 2 22. L = 160 cm 2 ; S ≈ 215.1 cm 2 23. L = 630 ft 2 ; S = 855 ft 2 24. L = 175π m 2 ; S = 224π m 2 25. L = 150π in 2 ; S = 250π in 2 26. S = 800 ft 2 27. S = 448π m 2 28. V = 1080 ft 3 29. V ≈ 1651.7 cm 3 30. V ...

3, with an ∠ of rotational symmetry of 120°. 47. 2a. yes; 120°; order: 3 2b. yes; 180°; order: 2° 2c. no 3a. line symmetry and rotational symmetry; 72°; order: 49. 51. A 53. C 55. 72 57. x = -4 59. x = 0 61. 7 63. $246.40 65. 5 cm 67. P′ (6, -5) 69. P′ (0,-4) 3b. line symmetry; 51.4°; order: 7 4a. both 4b. neither 12-...

of consecutive angles whose common side is a base of the trapezoid. ángulo base de un trapecio Uno de los dos ángulos consecutivos cuyo lado en común es la base del trapecio. base angle of an isosceles triangle (p. 273) One of the two angles that have the base of the triangle as a side. ángulo base de un triángulo isós...

indica que dos polígonos son congruentes enumerando los vértices en orden de correspondencia. congruence transformation (p. 824) See isometry. transformación de congruencia Ver isometría. congruent (p. 13) Having the same size and shape, denoted by ≅. congruente Que tiene el mismo tamaño y forma, expresado por ≅. S122 ...

. diámetro Segmento que atraviesa el centro de un círculo y cuyos extremos están sobre el círculo; longitud de dicho segmento. dilation (p. 495) A transformation in which the lines connecting every point P with its preimage P′ all intersect at a point C known as the center of dilation, and CP′ ___ CP is the same for ev...

S130 Glossary/Glosario a x _ _ = x b x 2 = ab x = √  ab The probability of the pointer landing on red is 2 __ . 9 ��...

tiene puntos espaciados uniformemente en un patrón triangular que se repite. isometry (p. 824) A transformation that does not change the size or shape of a figure. isosceles trapezoid (p. 429) A trapezoid in which the legs are congruent. isometría Transformación que no cambia el tamaño ni la forma de una figura. Refle...

lateral face. prisma oblicuo Prisma que tiene por lo menos una cara lateral no rectangular. obtuse angle (p. 21) An angle that measures greater than 90° and less than 180°. ángulo obtuso Ángulo que mide más de 90° y menos de 180°. obtuse triangle (p. 216) A triangle with one obtuse angle. triángulo obtusángulo Triángul...

ch distances are measured in a polar coordinate system. SPANISH polo Punto desde el que se miden las distancias en un sistema de coordenadas polares. EXAMPLES polygon (p. 98) A closed plane figure formed by three or more segments such that each segment intersects exactly two other segments only at their endpoints and n...

t. rotación Transformación sobre un punto P, también conocido como el centro de rotación, tal que cada punto y su imagen estén a la misma distancia de P. Todos los ángulos con vértice P formados por un punto y su imagen son congruentes. rotational symmetry (p. 857) A figure that can be rotated about a point by an angle...

° triangle or a 30°-60°-90° triangle. triángulo rectángulo especial Triángulo de 45°-45°-90° o triángulo de 30°-60°-90°. y = -2x + 4 The slope is -2. The y-intercept is 4. Glossary/Glosario S153 S153 �� ENGLISH sphere (p. 714) The set of points in space that ...

ectiva de dos puntos Dibujo en perspectiva con dos puntos de fuga. U undefined term (p. 6) A basic figure that is not defined in terms of other figures. The undefined terms in geometry are point, line, and plane. término indefinido Figura básica que no está definida en función de otras figuras. Los términos indefinidos...

kythera, 792 Antique speakers, 692 Apothem, 601 Applications Advertising, 499 Agriculture, 765 Animation, 53, 835, 842 Anthropology, 802 Archaeology, 262, 787, 793 Architecture, 47, 159, 166, 220, 324, 457, 467, 485, 529, 658, 667, 695, 706, 767, 843, 859, 875 Art, 10, 32, 167, 465, 483, 557, 593, 657, 668, 834, 849, 8...

, 185, 193, 218, 226, 245, 255, 262, 269, 276, 303, 310, 324, 335, 342, 352, 359, 385, 421, 431, 457, 473, 490, 497, 520, 546, 563, 593, 602, 608, 619, 633, 673, 683, 692, 700, 708, 717, 750, 766, 775, 786, 801, 826, 833, 850, 858, 866, 874 justify, 394, 801 list, 113, 148, 352 name, 8, 24, 218, 233, 593 sketch (draw),...

76, 880 Estimating area under curves, 621 Estimation, 25, 37, 41, 77, 108, 177, 195, 229, 278, 325, 361, 387, 433, 466, 492, 493, 538, 565, 611, 621, 676, 719, 768, 803, 844, 877, S52 rounding and, S52 Estimation strategies, 578–579 Euclid, 257, 460 Euler, Leonhard, 78 Euler line, 321 Euler’s Formula, 670 Event, 628 co...

tion, 278 Recreation, 92 Shuffleboard, 305 Sports, 19, 635 Surveying, 353, 556 Travel, 458 Literal equations, 41, 169, 588, 590 Locus, 300, 302, 304, 306, 600, 714, 743, 804 Logic puzzles, solving, 94–95 Logically equivalent statements, 83 Lune, 611 Lunette, 767 Luxor Hotel, 159 M Madurodam, 458 Magnitude of a vector, ...