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10. Draw a two-point perspective view. 11. Determine whether the drawing represents the given object. Find the number of vertices, edges, and faces of each polyhedron. Use your results to verify Euler’s formula. 12. 13. 14. Find the distance between the given points. Find the midpoint of the segment with the given end... |
the volume. Lesson 10-8 Find the surface area and volume of each figure. Give your answers in terms of π. 37. 38. 39. 40. The radius of a sphere with r = 24 cm is multiplied by 1 _ 3 surface area and volume.. Describe the effect on the 41. The radius of a sphere with r = 15 mm is multiplied by 4. Describe the effect o... |
29. ⊙B that passes through (3, 4) and has center B (-2, 1) Graph each equation. 30. (x + 3) 2 + (y - 4) 2 = 1 31. x 2 + (y + 4) 2 = 16 TEKS TAKS Practice S25 S25 �������������������������������������������������������������������������������������������������������������������������������������������������������������... |
on 12-3 Lesson 12-4 15. Copy the figure and draw two lines of reflection that produce an equivalent transformation. S26S26 TEKS TAKS Practice ����������������������������������������������������� Lesson 12-5 Describe the symmetry of each figure. Copy the shape and draw all lines of symmetry. If there is rotational symm... |
°, find m∠2, m∠3, and m∠4. (Lesson 1-4) � � � � Architecture Use the following information for Exercises 10 and 11. The bricks used to make a building are one-fourth as tall as they are wide, and the bricks are 2.25 inches tall. (Lesson 1-5) 4. What is the total distance from Austin to 10. What is the area of the large... |
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. (Lesson 2-1) 15,... |
have? Solve the equation for c and justify each step. (Lesson 2-5) 10. Travel On a city map, the library, post office, and police station are collinear points in that order. The distance from the library to the post office is 2.3 miles. The distance from the post office to the police station is 5.1 miles. Which theore... |
runs 10 miles by 3:00 P.M. and 25 miles by 4:30 P.M. Graph the line that represents her distance run. Find and interpret the slope of the line. (Lesson 3-5) 9. Business A cab company charges $8 per ride plus $0.25 per mile. Another cab company charges $5 per ride plus $0.35 per mile. For how many miles will two cab ri... |
on 4-6) 7. The first step in creating a Sierpinski triangle is to connect the midpoints of the sides of a triangle as shown. (Lesson 4-7) Given: ̶̶̶ ̶̶ ̶̶ AB ≅ HB ≅ HG, ∠GAB ≅ ∠BHG, ∠AGB ≅ ∠HBG ̶̶ AG Prove: △AGB ≅ △HBG 4. Sports A kite is made up of two pairs of congruent triangles. Use SAS to explain why △ABD ≅ △CBD. ... |
. Draw a sketch to show where the firehouse should be positioned. Justify your sketch. (Lesson 5-2) 3. Safety A lifeguard needs to watch three areas of a water park. Draw a sketch to show where she should stand to be the same distance from all the swimmers. Justify your sketch. (Lesson 5-2) 4. Art An artist is designin... |
�������� Chapter 6 Applications Practice 1. Safety A stop sign is in the shape of a regular octagon. What is the value of x? (Lesson 6-1) Design Use the following information for Exercises 7–9. 2. Hobbies Nancy is planting a garden shaped like a regular pentagon. She bought metal edging to surround the garden and preve... |
should she buy for the entire project? (Lesson 6-6) 13. Carpentry Aaron is building a shadow box for his baseball memorabilia. The shadow box will be in the shape of a trapezoid, as shown below. The wood for the box costs $1.59 per foot. Estimate the cost of the lumber. (Lesson 6-6) TEKS TAKS Practice S33 S33 ��������... |
the castle has a width of 40 ft and a length of 50 ft. The width of the great room of the dollhouse is 8 in. What is the length of the great room of the dollhouse? (Lesson 7-1) 6. Travel A map is a scale model of a real city. The scale on the map is 1 in.:30 mi. Two cities are 165 mi apart. How far apart will the citi... |
above the ground is the end of the ramp? Round to the nearest foot. (Lesson 8-2) 5. Running A race includes a 0.25-mile hill on which runners travel from 510 ft of elevation to 570 ft of elevation. What angle does the hill form? Round to the nearest degree. (Lesson 8-3) 7. Aviation A helicopter pilot flying at an alti... |
ecake pans with three diameters: 18 cm, 22 cm, and 26 cm. Find the area of the bottom of each pan. Round to the nearest square centimeter. (Lesson 9-2) 6. Recreation A track for a toy car is a 2 ft by 2 ft square with a semicircle at each end. What is the distance around the track? Round to the nearest foot. (Lesson 9-... |
shape of a cylinder. How can the dough be sliced to make circular cookies? (Lesson 10-1) 2. Recreation The tent shown is in the shape of a pentagonal prism. If a wall is used to divide the tent into two rooms, what shapes could the wall be? (Lesson 10-1) 7. Camping The tent structure shown is in the shape of a square ... |
3 soccer ball is 24 in. The circumference of a size 5 soccer ball is 28 in. How many times as great is the volume of a size 5 ball as the volume of a size 3 ball? (Lesson 10-8) TEKS TAKS Practice S37 S37 ������������������������������������������������������������������������������������������ Chapter 11 Applications ... |
to find each area to the nearest tenth for Exercises 11 and 12. A sprinkler system has three types of sprinkler heads: a quarter circle, a semicircle, and a full circle. The sprinkler will spray a distance of 15 feet from the sprinkler head. (Lesson 11-3) 11. What is the area of the sector that will be watered by the ... |
course has a barrier between the tee T and the hole H. Copy the figure and draw a diagram that shows how to make a hole in one. (Lesson 12-3) 5. Sports A team’s Web site shows a baseball moving across the screen. The ball is reflected over line ℓ and is then reflected over line m. Describe a single transformation that... |
Draw a circle. Add five points to the circle to represent the five people in the problem. Then draw segments to connect each point to each of the other four points. Count the number of segments in the final diagram. The total number of segments is the answer to the problem. It takes 10 pieces of ribbon to connect each... |
triangles are formed by cutting a rectangle along its diagonal. What possible shapes can be formed by arranging these triangles? 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 th... |
12 inches. PRACTICE 1. The sum of Cary’s age and his brother’s age is 34. The difference between their ages is 4. How old are Cary and his brother? 2. Adult tickets for a theater performance cost $8 and children’s tickets cost $3. A group with twice as many adults as children attends the performance and spends $133 on... |
starting with the dimensions you found for the first triangle, and confirm that the fifth triangle has a hypotenuse of 4 inches. PRACTICE 1. In a trivia game, each question is worth twice as many points as the one before it. Chelsea answers 5 questions and earns 1550 points. How many points was her first question wort... |
GDB = DAY to decode the sentence DQ DSSOH D GDB NHHSV WKH GRFWRU DZDB. 2. Describe the pattern 15, 22, 29, 36, 43,... and find the next two numbers. S44 S44 Problem-Solving Handbook ������������������1234 Make a Table To solve a problem that involves a relationship between two sets of numbers, you can make a table to ... |
gruent sides. How many possible shapes might Mary select? Problem-Solving Handbook S45 S45 1234 Solve a Simpler Problem A problem with many steps or involving very large numbers can be overwhelming. Sometimes it helps to solve a simpler problem first, or to break the complex problem into multiple simpler ones. Problem-... |
Reasoning Some problems provide clues and facts that you must use to find the solution. To use logical reasoning, identify 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 Reas... |
a pullover. Who wears the sweater and who wears the red top? 2. The Warriors, Jaguars, and Cougars each have a different-colored shape on their team shirt. The colors are green, purple, and red, and the shapes are a triangle, a rectangle, and a hexagon. The Warriors’ shape has the most sides, the color of the Jaguars’... |
2. A cupboard contains 12 cups, and each cup has a lid, a handle, or both. There are seven cups with handles, and three cups with both a lid and a handle. How many cups have only a lid? S48 S48 Problem-Solving Handbook ���������������������������������������������1234 Make an Organized List If a problem involves multi... |
pizza with one of each. How many combinations can you order? Problem-Solving Handbook S49 S49 1234 Skills Bank Operations with Real Numbers The four basic operations with real numbers are addition, subtraction, multiplication, and division. E X A M P L E Simplify each expression.5 · 3 3.5 · 3 = 10.5 B 0.5 - 4 0.5 - 4 ... |
0 · a = 0 Distributive a · (b + c) = a · b + a · c Transitive If a = b and b = c, then a = c. Other Real Number Properties E X A M P L E 1 Name the property shown. A 2 · (3 - 3) = 0 Multiplication Property of Zero B (9 + 3) + 2 = 9 + (3 + 2) Associative Property of Addition E X A M P L E 2 Give an example of each prop... |
3 < 5; round down. 33 2.2 E X A M P L E 2 Estimate each sum by rounding. A 12.75 + 15.94 13 + 16 29 Add. Round each number. B 182 + 208 + 319 180 + 210 + 320 Round each number. 710 Add. E X A M P L E 3 Tell whether an estimate is sufficient or an exact answer is needed. A The distance from San Antonio to Austin is abo... |
, -1, 0, 1, 2, …} 1 _ ⎬ ⎨, -3.4, 0 Write all of the names that apply to each number. A -79 real number, rational number, integer B √ 13 real number, irrational number PRACTICE Write all of the names that apply to each number. ̶ 2. 0. 1. 11 3 3. π 4. -4.6 5. 0 Exponents Exponents are used to describe repeated mul... |
each number in standard notation. A 2.99 × 10 4 B 3.04 × 10 -6 2.99 × 10,000 29,900 10 4 = 10,000 Move the decimal 3.04 × 0.000001 0.00000304 10 -6 = 0.000001 Move the decimal point 4 places right. point 6 places left. PRACTICE Write each number in standard notation. 1. 10 3 2. 10 8 4. 9.04 × 10 2 5. 9.0 × 10 -4 3. 10... |
0. The coordinate plane is formed by two perpendicular number lines, the x-axis and the y-axis, that intersect at the origin, (0, 0). The location of a point is described by an ordered pair, (x, y), where x is the distance from the y-axis and y is the distance from the x-axis. The coordinate plane is divided into four... |
more than an apple 2. 10 times as heavy as a horse 3. 3 years less than 9 times Gwen’s age Variables and Expressions A variable is a letter that represents a value that can change or vary. An algebraic expression has one or more variables. To evaluate an algebraic expression, substitute the given value for each variab... |
2 2 · u _ = 2 · 10 2 u = 20 _ 3 + n 8 = -2 Multiply both sides by 2. Add 4 to both sides. Divide both sides by 6 (-2) 3 + n = -16 - 3 ̶̶̶̶̶ - 3 ̶̶̶ n = -19 Multiply both sides by 8. Subtract 3 from both sides. 2. 2u = 6 3. n _ 3 = 21 4. 13 = x - 16 5. 1.5k = 27 6. 18 + p = 16 8. b - 2.7 = 3.4 9. 2w + 7 = 18 11. 4z - 8... |
greater than.” Use an empty circle for < or >. Shade the side of the line that contains the solutions. PRACTICE Write each expression as an inequality. Graph the inequality. 1. u is less than 0 2. n is greater than or equal to 15 3. x is less than 3 4. b is greater than 5 5. y is less than or equal to 4 6. m is greate... |
5. 2g + 13 ≥ -1 8. k _ 3 + 4 < 12 3. 6x ≥ 5x + 4 6. -4a ≥ 18 - w _ 9. 3 _ 4 4 ≥ 7 �������������������� Absolute Value The absolute value of a number is its distance from zero on the number line. The absolute value of a number a is represented by ⎜a⎟. E X A M P L E Simplify. A ⎜-4⎟ ⎜-4⎟ = 4 B ⎜3 - 9⎟ ⎜3 - 9⎟ = ⎜-6⎟ = 6... |
2. y 2 = x 5. 9y = 3 (0, 0), (1, 2), (0, 2) 3. S: ⎬ ⎨ (-5, 1), (-4, 1), (-3, 1) 6. S: ⎬ ⎨ Skills Bank S61 S61 ���������������������������������� Inverse Functions A function is a rule that relates two quantities, the input and the output. Each input value corresponds to only one output value. The inver... |
k is the constant of variation” is written as y = kx. E X A M P L E Find the constant of variation. A y varies directly as x, and y = 7 B t varies directly as c, and t = 1 when x = 3. y = kx 7 = k (3) 7 _ = k 3 Substitute 7 for y and 3 for x. when c = 0.1. t = kc (1) = k (0.1) Substitute 1 for t and 0.1 for c. Solve f... |
Translation y = ƒ (x - h) If h > 0, translate h units right. If h < 0, translate h units left. E X A M P L E Describe the transformation given by the equation y = (x - 3) 2. Step 1 Identify the parent function. The parent function is y = x 2. Step 2 Identify the transformation. The equation represents a horizontal tra... |
a 4 11. 2 - 4x 4. 12 S64 S64 Skills Bank Quadratic Functions A quadratic function is a function that can be written in the form y = a x 2 + bx + c, where a ≠ 0. The graph of a quadratic function is a parabola, an almost U-shaped graph. Graph of a Quadratic Function y = a x 2 + bx + c • If a > 0, the parabola opens upw... |
= 2x 2 + 4 4. y = 3 x 2 - 6x + 8 5. y = - 5x 2 + 10 6. y = 0.5x 2 + x + 2 Skills Bank S65 S65 ���������������������������� Factoring to Solve Quadratic Equations One method of solving quadratic equations is to apply the Zero Product Property, which states that if ab = 0, then a = 0 or b = 0. First write the quadratic ... |
�� (-4 ) 2 - 4 (1 ) (6 ) ___ 2 (1 ) x = x = 7 ± √ 25 _ 4 7 + 5 _ 4 or x = 7 - 5 _ 4 Simplify. Simplify. x = 4 ± √ -8 _ 2 Since you cannot take the square root of a negative number, there is no solution. x = 3 or x = 1 _ 2 Write the solution. PRACTICE Use the Quadratic Formula to solve each equation. 1. x 2 + ... |
first equation. Distribute 2. Simplify. Solve for x. Substitute 6 for x into the second equation and simplify. Simplify. Write the solution as an ordered pair. Multiply each term in the second equation by -2 to get opposite y-coefficients. Simplify. Write the system using the new equation so that like terms are aligne... |
for x. Check √ PRACTICE Solve each equation. Check your answer. 1. √ x + 1 = 4 3. √ 1 - x = 3 5. √ 7 + x = 0 7. √ 3 - 2x = 3 S68 S68 Skills Bank 2. √ 2x - 1 = 5 4. √ -6 - 5x = 2 6. √ 4x + 4 = 2 8. √ 60 - 2x = 8 ����������������������������������������������������� Matrix Operations... |
1 1. ⎢ 0 ⎣ ⎡ ⎤ 0 -1 ⎦ 4. ⎡ 1 ⎢ 0 ⎣ ⎡ ⎤ -1 -3 ⎦ ⎡ 0 7.5 0 ⎣ ⎦ ⎤ -9 ⎥ -1 ⎦ 2. 2 ⎢ 7 ⎣ ⎤ 2 ⎥ -1 ⎦ 8. ⎡ 8 ⎢ 0 ⎣ ⎡ ⎤ -2 -1 - ⎢ ⎥ 4 -3 ⎣ ⎦ ⎤ 1 ⎥ -7 ⎦ ⎡ 3 3. -. 1 _ ⎢ 2 0 ⎣ ⎤ -8 ⎥ 2 ⎦ Skills Bank S69 S69 Structure of Measurement Systems The metric system of measurement is used worldwide. In the United States, we most commonl... |
? The speed of the car is the ratio of the change in distance to the change in time. 1 km _ 5 min × 1000 m _ 1 km Convert km to m and min to s. × 1 min _ 60 s ≈ 3.33 m/s PRACTICE 1. The mass of a small meteor is decreasing at a rate of 6000 g every 2 min. What is the rate of decrease in kilograms per second? 2. The tem... |
68° F. Simplify. Substitute 20 for C. B 25 lb ≈ g 25 lb × 0.454 kg _ × 1 lb 1000 g _ 1 kg ≈ 11,350 g C 32 ft 2 ≈ m 2 32 ft 2 × 0.305 m _ × 0.305 m _ 1 ft ≈ 2.98 m 2 1 ft Use the conversion factor for pounds to kilograms. Then convert kilograms to grams. The units are squared, so apply the conversion factor for feet to... |
from 3.729 lb to 3.731 lb Step 1: Find the most accurate measurement. The most accurate measurement is the measurement closest to the actual weight of 3.72 lb. 3.718 ± 0.002 lb Step 2: Find the most precise measurement. The most precise measurement is the measurement (not the tolerance) with the most decimal places. 3... |
.0196 absolute error = 5.5 ft - 5.1 ft = 0.4 ft relative error = 5.5 ft-5.1 ft __ = 0.0784 5.1 ft percent error = -1.96% percent error = 7.84% PRACTICE Find the absolute, relative, and percent errors. The first value is the actual value, and the second is the measured value. 1. 1.23, 1.00 3. 5.55, 6.00 2. 123, 100 Sign... |
Sun (inches, feet, yards, miles) 3. the length of a decade (seconds, minutes, hours, years) Nonstandard Units There are several nonstandard unit systems. pH, a measure of the concentration of hydrogen ions in a solution, ranges from 0 to 14. Pure water has a pH of 7, which is considered neutral. A pH less than 7 is ac... |
of your Geometry book. 2. Use a stopwatch to measure the time it takes to climb a set of stairs. 3. Use a tape measure to find the height of your classroom doorway. Choose Appropriate Measuring Tools To choose an appropriate measuring tool, consider the following criteria: • How large is the quantity being measured? •... |
7, 8, 8, 8, 8, 9} To find the median, locate the middle term. Since there are 30 terms, the median will be the average of the 15th and 16th terms. {0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9} 15 terms 4 + 5 = 9 _ _ 2 2 median = 4.5 Step 3: Find the mode. 15 terms The 15th ... |
E Find the probability of rolling each sum with two number cubes. The two number cubes are independent. In order to roll a 2, both number cubes need to show 1. So there is one possible way to roll a 2. To roll a 3, the first cube can show 1 and the second cube can show 2, or the first cube can show 2 and the second cu... |
% on a Language Arts test, 67% on a History test, 78% on a Science test, 82% on a Spanish test, and 90% on a Geometry test. Test Percent History Science Language Arts Spanish Geometry 67% 78% 81% 82% 90% List each test and its percent score. The table shows that Rick did very well on his Geometry test, but needs to imp... |
Time (min) Test Score Graph the ordered pairs (time, score) on a graph using a reasonable scale. Draw a trend line. 0 60 180 160 100 30 15 45 15 0 60 120 90 45 30 50 60 95 100 90 70 60 80 50 60 75 85 80 70 65 The trend line indicates that a student’s scores improved as study time increased. PRACTICE Make a scatter plo... |
ACTICE 1. Make a box-and-whisker plot of the data set. 12 18 10 17 18 15 17 13 7 14 19 Circle Graphs Circle graphs are used to represent data as percentages of the total. To draw a circle graph, convert the data to percentages, and then make a section of the circle for each category. E X A M P L E 1 Make a circle graph... |
overlapping region. Write factors in one set only in the non-overlapping parts. PRACTICE Draw a Venn diagram to show the relationship between the following sets. 1. factors of 9 and factors of 8 2. factors of 36 and factors of 30 3. factors of 60 and factors of 72 Skills Bank S81 S81 ����������������������������������... |
of the hypotenuse. (Pyth. Thm.; p. 45) Chapter 2 Thm. 2-6-1 Linear Pair Theorem If two angles form a linear pair, then they are supplementary. (Lin. Pair Thm.; p. 110) Thm. 2-6-2 Congruent Supplements Theorem If two angles are supplementary to the same angle (or to two congruent angles), then the two angles are congru... |
. Thm.; p. 156) Thm. 3-2-4 Same-Side Interior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary. (Same-Side Int. Thm.; p. 156) Post. 3-3-1 Converse of the Corresponding Angles Postulate If two coplanar lines are cut by a transversal so t... |
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 and only if they have the same slope. Any two vertical lines are parallel. (ǁ Lin... |
included side of another triangle, then the triangles are congruent. (ASA; p. 252) Thm. 4-5-2 Angle-Angle-Side (AAS) Congruence Theorem If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent. (AAS; p. 254... |
and Corollaries S83 S83 Thm. 5-1-4 Converse of the Angle Bisector Thm. 5-7-2 Pythagorean Inequalities Theorem If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle. (Conv. of ∠ Bisector Thm.; p. 301) Theorem In △ABC, c is the length of the longest si... |
333) Thm. 5-5-3 Triangle Inequality Theorem The sum of any two side lengths of a triangle is greater than the third side length. (△ Inequal. Thm.; p. 334) Thm. 5-6-1 Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer thir... |
. ( → opp. ≅; p. 392) Thm. 6-2-3 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. ( → cons. supp.; p. 392) Thm. 6-2-4 If a quadrilateral is a parallelogram, then its diagonals bisect each other. ( → diags. bisect each other; p. 392) Thm. 6-3-1 If one pair of opposite sides of... |
ombus → ; p. 409) Thm. 6-4-4 If a parallelogram is a rhombus, then its diagonals are perpendicular. (rhombus → diags. ⊥; p. 409) Thm. 6-4-5 If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles. (rhombus → each diag. bisects opp. ; p. 409) Thm. 6-5-1 If one angle of a parallelogram is ... |
. 429) Thm. 6-6-4 If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. (trap. with pair base ≅ → isosc. trap.; p. 429) Thm. 6-6-5 A trapezoid is isosceles if and only if its diagonals are congruent. (isosc. trap ↔ diags. ≅; p. 429) Thm. 6-6-6 Trapezoid Midsegment Theorem The midsegme... |
Triangle Angle Bisector Theorem An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides. (△ ∠ Bisector Thm.; p. 483) Thm. 7-5-1 Proportional Perimeters and Areas Theorem If the similarity ratio of two similar figures is a __, then... |
-2 If a line is perpendicular to a radius of a circle at a point on the circle, then the line is tangent to the circle. (line ⊥ to radius → line tangent to ⊙; p. 748) Thm. 11-1-3 If two segments are tangent to a circle from the same external point, then the segments are congruent. (2 segs. tangent to ⊙ from same ext. p... |
775) Thm. 11-5-1 If a tangent and a secant (or chord) intersect on a circle at the point of tangency, then the measure of the angle formed is half the measure of its intercepted arc. (p. 782) Thm. 11-5-2 If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the s... |
of rotation is twice the measure of the angle formed by the lines. (p. 849) Thm. 12-4-3 Any translation or rotation is equivalent to a composition of two reflections. (p. 850) Constructions Angle Bisector............................. p. 23 Parallel Lines............... pp. 163, 170, 171, 179 Center of a Circle........... |
... pp. 824, 829 Regular Decagon......................... p. 381 Regular Dodecagon....................... p. 380 Regular Hexagon......................... p. 380 Regular Octagon. 380 Regular Pentagon. 381 Rhombus.......................... pp. 415, 424 Using ASA............................ p. 253 Right Triangle............. |
..................... p. 779 Irrational Numbers....................... p. 363 Translation........................ pp. 831, 836 Kite..................................... p. 435 Triangle Circumscribed Midpoint..................................p. 16 Midsegment of a Triangle. 327 Orthocenter of a Triangle..................... |
median: 0.442; mode: 0.44 47. Mother is 36; 1-2 Check It Out! 1a. 3 1 __ 2 1b. 4 1 __ 2 3a. 1 2 __ 3 3b. 24 4. 591.25 m 5. RS = 4; ST = 4; RT = 8 ̶̶̶ MY 3. 3.5 ̶̶̶ XM and Exercises 1. 7. 29 9. x = 4; KL = 7; JL = 14 11. 5 11 __ 12 15. 5 17. DE = EF =14; DF = 28 19a. C is the mdpt. of b. 16 21. 7.1 23. 4 25. S 27. Stat... |
must measure less than 90°. 47. 36° or 4° 49. 8100 51. 22.4 53. 55. 57. 6 1-4 Check It Out! 1a. adj.; lin. pair 1b. not adj. 1c. not adj. 2a. (102 - 7x) ° 2b. 63 1 __ 2 ° 3. 68° 4. m∠1 = m∠2 = 62.4°; m∠4 = 27.6° 5. Possible answer: ∠EDG and ∠FDH; m∠EDG ≈ m∠FDH ≈ 45° Exercises 1. (90 - x) °; (180 - x) ° 3. adj.; lin.... |
� 201.1 cm 2 11. P = 4x + 12; A = x 2 + 6x 13. 72 in 2 15. C ≈ 39.3 ft; A ≈ 122.7 ft 2 17. 82.81 yd 2 19. 6.1875 in 2 21. 17.1 cm 23. Statement A 25. 9 y 2 π 27. For a square, the length and width are both s, so P = 2l + 2w = 2s + 2s = 4s and A = lw = s (s) = s 2. 29. b = 41 in.; h = 38 in. 31a. ac + ad + bc + bd b. (a... |
= MC = 5.0 ft; mdpt. of MB = MD ≈ 6.4 ft. 35. G 37. J 39. ±2 41. AB = √ x 2 + y 2 43. yes 45. 90°; rt. 47. 135°; obtuse 49. 4 ft 2 ��������������� 1-7 Check It Out! 1a. translation; MNOP → M′N′O′P′ 1b. rotation; △XYZ → △X′Y′Z′ 2. rotation; 90° 3. J′ (-1, -5) ; K′ (1, 5) ; L′ (1, 0) ; M′ (-1, 0) 4. (x, y) → (x - 4,... |
1 38. 90° rotation; DEFG → D′E′F′G′ 39. translation; PQRS → P′Q′R′S′ 40. X′ (-1, 1) ; Y′ (1, 4) ; Z′ (2, 3) 19. B 21. D 23. R′ (-1, -12) ; S′ (-3, -9) ; T ′ (-7, -7) 25. 29. A 31. A 33a. R″ (1, 0) ; S″ (0, 3) ; T′′ (4, 3) b. (x, y) → ( x + 3, y + 2) 35. 37. (-x, y) 39. x = -6 or x = 3 41. x = 1 or x = 2 43. 13.9° 45. 4... |
m∠CBA; AC = CB 45. yes 47. no 49. 10x - 6 51. 6πx 53. (3, -2), (4, 0), (8, -1) 2-2 10. 3.5 11. 5 12. 7.6 13. 22 14. 13; 13; 26 15. 18; 18; 36 16. ∠VYX: rt.; ∠VYZ: obtuse; ∠XYZ: Check It Out! 1. Hypothesis: A number is divisible by 6. Conclusion: A number is divisible by 3. 2. If 2 are comp., then they are acute. 3. ... |
57. 3 59. y = 2x + 1 61. T 63. T 65. 2 __ 81 2-3 Check It Out! 1. deductive reasoning 2. valid 3. valid 4. Polygon P is not a quad. Exercises 3. deductive reasoning 5. valid 7. invalid 9. deductive reasoning 11. invalid 13. Dakota gets better grades in Social Studies. 15. valid 17. valid 19. yes; no; because the first... |
: If you drop your prescription off by 8 A.M., then your medicine will be ready by 5 P.M. 5. Converse: If 2 segs. are ≅, then they have the same length. Biconditional: 2 segs. have the same length if and only if they are ≅. 7. F 9. An animal is a hummingbird if and only if it is a tiny, brightly colored bird with narro... |
32) (Subst.); C = 5 __ 9 (54) (Simplify.); C = 30 (Simplify.) 3. ∠ Add. Post.; Subst.; Simplify.; Subtr. Prop. of =; Mult. Prop. of = 4a. Sym. Prop. of = 4b. Reflex. Prop. of = 4c. Trans. Prop. of = 4d. Sym. Prop. of ≅ Exercises 3. t - 3.2 = -8.3 (Given); t = -5.1 (Add. Prop. of =) 5. x + 3 ____ -2 = 8 (Given); x + 3 ... |
S90 S90 Selected Answers 25. Sym. Prop. of ≅ 27. Trans. Prop. of = 29. x = 16; 2 (3.1x - 0.87) = 94.36 (Given); 6.2x - 1.74 = 94.36 (Distrib. Prop.); 6.2x = 96.1 (Add. Prop. of =); x = 15.5 (Div. Prop. of =); possible answer: the exact solution rounds to the estimate. 31. ∠A ≅ ∠T 33. x + 1 ____ 2 x + 1 = 6 (Mult. Prop... |
b. m∠1 + m∠2 = m∠2 + m∠3 2c. Subtr. Prop. of = 2d. ∠1 ≅ ∠3 3. 1. ∠1 and ∠2 are comp. ∠2 and ∠3 are comp. (Given) 2. m∠1 + m∠2 = 90°, m∠2 + m∠3 = 90° (Def. of comp. ) 3. m∠1 + m∠2 = m∠2 + m∠3 (Subst.) 4. m∠2 = m∠2 (Reflex. Prop. of =) 5. m∠1 = m∠3 (Subtr. Prop. of =) 6. ∠1 ≅ ∠3 (Def. of ≅ ) Exercises 1. statements; re... |
� segs.) ̶̶ AB ≅ ̶̶ BE ≅ 9. 1. Exercises 1. flowchart 3. 1. ∠1 ≅ ∠2 (Given) 2. ∠1 and ∠2 are supp. (Lin. Pair Thm.) 3. ∠1 and ∠2 are rt. . (≅ supp. → rt. ) 5. 1. ∠2 ≅ ∠4 (Given) ̶̶ AB ≅ 2. ∠1 ≅ ∠2, ∠3 ≅ ∠4 (Vert. Thm.) 3. ∠1 ≅ ∠4 (Trans. Prop. of ≅) 4. ∠1 ≅ ∠3 (Trans. Prop. of ≅) ̶̶ AC. (Given) 7. 1. B is the mdp... |
(Subst.) 5. ∠1 ≅ ∠3 (Given) 6. m∠1 = m∠3 (Def. of ≅ ) 7. m∠2 + m∠1 = 90° (Subst.) 8. ∠1 and ∠2 are comp. (Def. of comp. ) 4. It is given that ∠1 ≅ ∠4. By the Vert. Thm., ∠1 ≅ ∠2 and 9. 1. ∠1 ≅ ∠4 (Given) 2. ∠1 ≅ ∠2 (Vert. Thm.) 3. ∠4 ≅ ∠2 (Trans. Prop. of ≅) 4. m∠4 = m∠2 (Def. of ≅ ) 5. ∠3 and ∠4 are supp. (Lin... |
, and 94° 29. (-4, 5) SGR 1. theorem 2. deductive reasoning 3. counterexample 4. conjecture 5. The rightmost △ is duplicated, rotated 180°, and shifted to and 1. 7. The white section 6. Each item is 1 __ 6 greater than the previous one. The next 2 items are 5 _ 6 is halved. If the white section is a rect. but not a squ... |
35. m ___ -5 + 3 = -4.5 (Given); m ___ -5 = -7.5 (Subtr. Prop. of =); m = 37.5 (Mult. Prop. of =) 36. -47 = 3x - 59 (Given); 12 = 3x (Add. Prop. of =); 4 = x (Div. Prop. of =) 37. Reflex. Prop. of = 38. Sym. Prop. of ≅ 39. Trans. Prop. of = 40. figure ABCD 41. m∠5 = ̶̶ ̶̶ m∠2 42. EF 43. I = Prt CD ≅ (Given) ; 4200 = P... |
2d. ∠2 and ∠3 3. transv. n; same-side int. ̶̶ FJ 1d. plane FJH ǁ plane ̶̶ AB and ̶̶ AB and Exercises 1. alternate interior angles 3–9. Possible answers ̶̶̶ given. 3. DH are skew. 5. plane ABC ǁ plane EFG 7. ∠6 and ∠8 9. ∠2 and ∠3 11. transv. m; alt. ext. 13. transv. p, sameside int. 15–21. Possible answers given... |
: ∠9 and ∠16, ∠12 and ∠13; transv. p: ∠1 and ∠14, ∠2 and ∠13; transv. q: ∠3 and ∠16, ∠4 and ∠15 53. corr. 55. -3; -7; -3; 9; 29 57. -8; -9; -8; -5; 0 59. C = 11.9 m; A = 11.3 m 2 61. Lin. Pair Thm. 3-2 Check It Out! 1. m∠QRS = 62° 2. m∠ABD = 60° 3. 55° and 60° Exercises 1. m∠JKL = 127° 3. m∠1 = 90° 5. x = 8; y = 9 7.... |
≅ ∠3, so ℓ ǁ m by the Conv. of Corr. Post. 1b. m∠7 = 77° and m∠5 = 77°, so ∠7 ≅ ∠5. ℓ ǁ m by the Conv. of Corr. Post. 2a. ∠4 ≅ ∠8, so r ǁ s by the Conv. of Alt. Int. Thm. 2b. m∠3 = 100° and m∠7 = 100°, so ∠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 a... |
≅ ∠8. r ǁ s by the Conv. of Alt. Int. Thm. 9. m∠2 = 132°, and m∠6 = 132°, so ∠2 ≅ ∠6. r ǁ s by the Conv. of Alt. Ext. Thm. 11. m∠1 = 60°, and m∠2 = 60°, so ∠1 ≅ ∠2. By the Conv. of Alt. Int. Thm., the landings are ǁ. 13. m∠4 = 54°, and m∠8 = 54°, so ∠4 ≅ ∠8. ℓ ǁ m by the Conv. of Corr. Post. 15. m∠1 = 55°, and... |
-Side Int. Thm. 37a. ∠URT ; m∠URT = m∠URS + m∠SRT by the ∠ Add. Post. It is given that m∠SRT = 25° and m∠URS = 90°, so m∠URT = 25° + 90° = 115°. b. It is given that m∠SUR = 65°. From part a, m∠URT = 115°. 65° + 115° = 180°, so SU ǁ RT by the Conv. of Same- ̶̶ DJ ǁ S92 S92 Selected Answers ������������������... |
ǁ. 55. By the Vert. Thm., ∠6 ≅ ∠3, so m∠6 = m∠3. It is given that m∠2 + m∠3 = 180°. By subst., m∠2 + m∠6 = 180°. By the Conv. of Same-Side Int. Thm., ℓ ǁ m. 57. a = b - c ̶̶ 59. y = - 3 __ 2 x + 3 63. BC ̶̶ 65. AD ̶̶ AB ⊥ ̶̶ AD ǁ 3-4 Check It Out! 1a. 2. 1. ∠EHF ≅ ∠HFG (Given) ̶̶ AB 1b. x < 17 2. EH ǁ FG... |
QR QR. Since It is given that ̶̶ ̶̶ RS by the ⊥ Transv. ⊥ PS ⊥ ̶̶ Thm. b. It is given that QR ̶̶ QR ⊥ ̶̶ PQ ǁ ̶̶ PS ǁ ̶̶ PS ǁ ̶̶ RS, ̶̶ PQ ⊥ ̶̶ PQ. So ̶̶ PS by the ̶̶ QR ⊥ and ⊥Transv. Thm. 25. Possible answer: 1.6 cm 31. C 33. D 35a. n ⊥ p b. AB; AB; the shortest distance from a point to a line is measured along a pe... |
-intercept form of an equation is solved for y. The x term is first, and the constant term is second. 3. y - 2 = 3 __ 4 (x + 4) 7. 5. 9. intersect 11. ǁ 13. y + 2 = 2x 15. y + 4 = 2 __ 3 (x - 6) 17. 19. intersect 21. coincide 23. $1000 per week 33. no 35. yes 37. ǁ line: y = 3x - 3; ⊥ line: y = - 1 __ 3 x + 11 __ 3 39.... |
5 = 107°, so ∠1 ≅ ∠5. c ǁ d by the Conv. of Corr. Post. 20. m∠6 = 66°, m∠3 =114°, and 66° + 114° ≠ 180°, so ∠6 and ∠3 are supp. c ǁ d by the Conv. of Same-Side Int. Thm. 21. m∠1 ≠ 99°, and m∠7 = 99°, so ∠1 ≅ ∠7. c ǁ d by the Conv. of Alt. Ext. Thm. 22. ̶̶̶ KM 23. x < 13 ̶̶ AD ⊥ ̶̶ BC, ̶̶ BC 24. 1. ̶̶ AB, ̶̶ DC ⊥ ... |
ene 35. S 37. A 41. D 43. D 45. It is an isosc. △ since 2 sides of the △ have length a. It is a rt. △ since 2 sides of the △ lie on the coord. axes and form a rt. ∠. 47. y = -3 49. y = x 2 51. y = x 2 53. T 55. ǁ 57. coincides 4-2 Check It Out! 1. 32° 2a. 26.3° 2b. (90 - x) ° 2c. 41 3 __ 5 ° 3. 141° 4. 32°; 32° Exercis... |
AC ≅ EC, 2. ∠BCA ≅ ∠ECD (Vert. are ≅.) 3. ∠ABC ≅ ∠DEC (Third Thm.) 4. 5. bisects ̶̶ 6. BC ≅ bisector) 7. △ABC ≅ △DEC (Def. of ≅ ) ̶̶ DC (Def. of ̶̶ BE, and ̶̶ BE 4. 1. ̶̶ JK ǁ ̶̶̶ ML (Given) ̶̶̶ ML (Given) 2. ∠KJN ≅ ∠MLN, ∠JKN ≅ ∠LMN (Alt. Int. Thm.) 3. ∠JNK ≅ ∠LNM (Vert. Thm.) 4. 5. bisects ̶̶ 6. JN ≅ bisect... |
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