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...... 746 secant segment............. 793 arc......................... 756 external secant segment..... 793 sector of a circle............ 764 arc length.................. 766 inscribed angle............. 772 segment of a circle.......... 765 central angle............... 756 intercepted arc............. 772 semicircle... |
the center of a circle is called a(n)?. ̶̶̶̶ 3. The measure of a(n)? is 360° minus the measure of its central angle. ̶̶̶̶? are coplanar circles with the same center. ̶̶̶̶ 4. 11-1 Lines That Intersect Circles (pp. 746–754) TEKS G.1.A, G.2.A, G.2.B, G.9.C E X A M P L E S ■ Identify each line or segment that intersects ⊙... |
m ⁀ BF ∠BAF and ∠FAE are supplementary, so m∠BAF = 180° - 62° = 118°. m ⁀ BF = m∠BAF = 118° ■ m ⁀ DF Since m∠DAE = 90°, m ⁀ DE = 90°. m∠EAF = 62°, so m ⁀ EF = 62°. By the Arc Addition Postulate, m ⁀ DF = m ⁀ DE + m ⁀ EF = 90° + 62° = 152°. EXERCISES Find each measure. 11. m ⁀ KM 12. m ⁀ HMK 13. m ⁀ JK 14. m ⁀ MJK Find... |
, G.9.C E X A M P L E S Find each measure. ■ m∠ABD By the Inscribed Angle Theorem, m∠ABD = 1 __ 2 m ⁀ AD, so m∠ABD = 1 __ 2 (108°) = 54°. ■ m ⁀ BE By the Inscribed Angle Theorem, m∠BAE = 1 __ 2 m ⁀ BE. So 28° = 1 __ 2 m ⁀ BE, and m ⁀ BE = 2 (28°) = 56°. EXERCISES Find each measure. 21. m ⁀JL 22. m∠MKL Find each value. ... |
TEKS G.1.A, G.2.B, G.5.A EXERCISES Find the value of the variable and the length of each chord. 29. 30. Find the value of the variable and the length of each secant segment. 31. 32. E X A M P L E S ■ Find the value of x and the length of each chord. AE ⋅ EB = DE ⋅ EC 12x = 8 (6) 12x = 48 x = 4 AB = 12 + 4 = 16 DC = 8 ... |
+ 2)2 + (y - 2)2 = 1. Study Guide: Review 813 813 ����������������������������������������������������������������������������������������� 1. Identify each line or segment that intersects the circle. 2. A jet is at a cruising altitude of 6.25 mi. To the nearest mile, what is the distance from the jet to a point on Ea... |
the SAT Mathematics Subject Tests vary only slightly each time the test is administered. You can find out the general distribution of questions across topics, then determine which areas need more of your attention when you are studying for the test. You may want to time yourself as you take this practice test. It shou... |
ers. Test writers create distracters by using common errors that students make. Be sure you always check your answer. The answer you get when you solve the problem may be one of the answer choices, but it may not be the correct answer. ̶̶̶ CD is tangent to ⊙B at C, and m ⁀ AC = 65°. What is m∠ABC? 130° 65° 32.5° 25° Lo... |
How do you determine the measure of the central angle? 9. Describe the errors a student might make to 1. What common error do the coordinates in get each of the distracters. choice B represent? 2. The y-coordinate in choice C is correct, but the x-coordinate is not. What error was made in finding the x-coordinate? 3. ... |
Use the diagram for Items 7 and 8. 2.5 feet 5.0 feet 8.4 feet 9.0 feet 2. What is the area of the polygon with vertices A (2, 3), B (12, 3), C (6, 0), and D (2, 0)? 12 square units 30 square units 21 square units 42 square units 7. What is m ⁀ QU? Use the diagram for Items 3–5. 25° 42° 58° 71° 8. Which expression can ... |
in words how you determined your answer. 11. Kite PQRS has diagonals ̶̶ PR and ̶̶ QS that intersect at T. Which of the following is the shortest ̶̶ PR? segment from Q to ̶̶ PT ̶̶ QP ̶̶ RQ ̶̶ TQ 12. If the perimeter of an equilateral triangle is reduced by a factor of 1 __, what is the effect on 2 the area of the trian... |
= 9, HJ = 5x -1, and LM = 13. What must be the value of x to prove that △HGJ and △LMK are congruent by SAS? 17. If the length of a side of a regular hexagon is 2, what is the area of the hexagon to the nearest tenth? 18. What is the arc length of a semicircle in a circle with radius 5 millimeters? Round to the nearest... |
1) Congruent Figures 6. (-3, 2) 9. (-1, -3) 7. (4, 3) 10. (-2, 0) Can you conclude that the given triangles are congruent? If so, explain why. 11. △PQS and △PRS 12. △DEG and △FGE Identify Similar Figures Can you conclude that the given figures are similar? If so, explain why. 13. △JKL and △JMN 14. rectangle PQRS and re... |
generalizations about geometric properties … G.5.C Geometric patterns* use properties of transformations ★ ★ ★ ★ ★ and their compositions to make connections between mathematics and the real world such as tessellations G.7.A Dimensionality and the geometry of location* use one- ★ ★ ★ ★ and two-dimensional coordinate s... |
justify properties of geometric figures.... Objective Identify and draw reflections. Vocabulary isometry Who uses this? Trail designers use reflections to find shortest paths. (See Example 3.) An isometry is a transformation that does not change the shape or size of a figure. Reflections, translations, and rotations a... |
across the line. E X A M P L E 3 Problem-Solving Application A trail designer is planning two trails that connect campsites A and B to a point on the river. He wants the total length of the trails to be as short as possible. Where should the trail meet the river? Understand the Problem The problem asks you to locate p... |
1, 5) Graph the preimage and image. 4. Reflect the rectangle with vertices S (3, 4), T (3, 1), U (-2, 1), and V (-2, 4) across the x-axis. THINK AND DISCUSS 1. Acute scalene △ABC is reflected across ̶̶ BC. Classify quadrilateral ABA'C. Explain your reasoning. 2. Point A' is a reflection of point A across line ℓ. What i... |
PRACTICE AND PROBLEM SOLVING Tell whether each transformation appears to be a reflection. 13. 15. 14. 16. Independent Practice For See Exercises Example 13–16 17–18 19 20–23 1 2 3 4 TEKS TEKS TAKS TAKS Skills Practice p. S26 Application Practice p. S39 12-1 Reflections 827 827 ������������������������� Multi-Step Copy... |
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 ... |
A'DB', which makes it possible to prove that △ADB ≅ △A'DB'. Finally use CPCTC to conclude that ̶̶̶ AA' and ̶̶̶ BB' as shown. First prove ̶̶ AB ≅ ̶̶̶ A'B'. � � �� � � � �� Once you have proved that the reflection image of a segment is congruent to the preimage, how could you prove the following? Write a plan for each pr... |
(See Example 4.) Also G.2.A, G.2.B, G.7.A A translation is a transformation where all the points of a figure are moved the same distance in the same direction. A translation is an isometry, so the image of a translated figure is congruent to the preimage. E X A M P L E 1 Identifying Translations Tell whether each tran... |
IZONTAL TRANSLATION ALONG VECTOR 〈a, 0〉 VERTICAL TRANSLATION ALONG VECTOR 〈0, b〉 GENERAL TRANSLATION ALONG VECTOR 〈a, b〉 832 832 Chapter 12 Extending Transformational Geometry ������������������������������������������������������������������������������������������������������������������������������������������������... |
) = (8, -16). The vector that moves her directly from her starting position to her final position is 〈16, 0〉 + 〈0, -24〉 = 〈16, -24〉. 4. What if…? Suppose another drummer started at the center of the field and marched along the same vectors as above. What would this drummer’s final position be? THINK AND DISCUSS 1. Poin... |
of the fourth polygon in the pattern? PRACTICE AND PROBLEM SOLVING Tell whether each transformation appears to be a translation. 11. 13. 13. 12. 14. 833 Independent Practice For See Exercises Example 11–14 15–16 17–19 20 1 2 3 4 TEKS TEKS TAKS TAKS Skills Practice p. S26 Application Practice p. S39 834 834 Chapter 12 ... |
P is on an axis. c. The image of P is at the origin. 24. This problem will prepare you for the Multi-Step TAKS Prep on page 854. The figure shows one hole of a miniature golf course and the path of a ball from the tee T to the hole H. a. What translation vector represents the path of the ball from T to ̶̶ DC? b. What ... |
given segment (see page 13) to construct the translation of each figure along a vector. 36. a point 37. a segment 38. a triangle 39. What is the image of P (1, 3) when it is translated along the vector 〈-3, 5〉? (0, 4) (-2, 8) (0, 6) (1, 3) 40. After a translation, the image of A (-6, -2) is B (-4, -4). What is the ima... |
B'. 46. If ∠A'B'C' is a translation of ∠ABC, then m∠ABC = m∠A'B'C'. 47. The translation △A'B'C' is congruent to the preimage △ABC. 48. If point C is between points A and B, then the translation C' is between A' and B'. 49. If points A, B, and C are collinear, then the translations A', B', and C' are collinear. SPIRAL R... |
= - x 2 graph: function rule: y = (x - 3) 2 + 2 graph: Try This TAKS Grades 9–11 Obj. 2, 5 For each parent function, write a function rule for the given transformation and graph the preimage and image. 1. parent function: y = x 2 transformation: a translation down 1 unit and right 4 units 2. parent function: y = √x t... |
Rotations A rotation is a transformation about a point P, called the center of rotation, such that each point and its image are the same distance from P, and such that all angles with vertex P formed by a point and its image are congruent. In the figure, ∠APA' is the angle of rotation. E X A M P L E 2 Drawing Rotation... |
the angle of rotation. Five seconds is 5 __ 40 = 1 __ 8 of a complete revolution, or 1 __ 8 (360°) = 45°. Step 2 Draw a right triangle to represent the car’s location (x, y) after a rotation of 45° about the origin. To review the sine and cosine ratios, see Lesson 8-2, pages 525–532. Step 3 Use the cosine ratio to fin... |
) ; 90° 9. D (2, 3), E (-1, 2), F (2, 1) ; 180° 10. P (-1, -1), Q (-4, -2), R (0, -2) ; 180 11. Animation An artist uses a coordinate plane to plan the motion of p. 841 an animated car. To simulate the car driving around a curve, the artist places the car at the point (10, 0) and then rotates it about the origin by 30°... |
to the nearest degree. b. Find the coordinates of the image of point Q. Round to the nearest tenth. Rectangle RSTU is the image of rectangle LMNP under a 180° rotation about point A. Name each of the following. 27. the image of point N 28. the preimage of point S 29. the image of ̶̶̶ MN 30. the preimage of ̶̶ TU 31. T... |
Explain. �� � � Use the figure for Exercises 38–40. 38. Sketch the image of pentagon ABCDE under a rotation of 90° about the origin. Give the vertices of the image. 39. Sketch the image of pentagon ABCDE under a rotation of 180° about the origin. Give the vertices of the image. 40. Write About It Is the image of ABCDE... |
̶ AB, then AB = A'B'. ̶̶̶ A'B' is a rotation of 47. If 48. If ∠A'B'C' is a rotation of ∠ABC, then m∠ABC = m∠A'B'C'. 49. The rotation △A'B'C' is congruent to the preimage △ABC. 50. If point C is between points A and B, then the rotation C' is between A' and B'. 51. If points A, B, and C are collinear, then the rotations... |
the number of rows and columns and then enter the values. Matrix operations can be used to perform transformations. Activity 1 1 Graph the triangle with vertices (1, 0), (2, 4), and (5, 3) on graph paper. Enter the point matrix that represents the vertices into matrix [B] on your calculator. ⎡ 1 2 Enter the matrix ⎢ ⎣... |
, 1), and (1, 2) on graph paper. Enter the 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... |
. Step 1 Draw △A'B'C', the reflection image of △ABC. Step 2 Translate △A'B'C' along find the final image, △A''B''C''. v to 848 848 Chapter 12 Extending Transformational Geometry ���������������������������������������������������������������������������������������������������������������������������������� B △RST ha... |
. By Theorem 12-4-2, the composition of two reflections across intersecting lines is equivalent to a rotation about the point of intersection. Since the lines are perpendicular, they form a 90° angle. By Theorem 12-4-2, the angle of rotation is 2 · 90° = 180°. 2. What if…? Suppose Tabitha reflects the figure across lin... |
��������������� 12-4 Exercises Exercises KEYWORD: MG7 12-4 KEYWORD: MG7 Parent GUIDED PRACTICE 1. Vocabulary Explain the steps you would use to draw a glide reflection Draw the result of each composition of isometries. p. 848 2. Translate △DEF along u and then reflect it across line ℓ. 3. Reflect rectangle PQRS acros... |
one more space. a. Describe a knight’s move as a composition of transformations. b. Copy the chessboard with the knight. Label all the positions the knight can reach in one move. c. Label all the positions the knight can reach in two moves. Copy each figure and draw two lines of reflection that produce an equivalent t... |
(-3, -2), S (-1, -2), and T (-1, 0). The vertices of △R'S'T'are R' (2, 2), S' (4, 2), and T'(4, 0). Describe the reflection and translation that make up the glide reflection. 852 852 Chapter 12 Extending Transformational Geometry 22. This problem will prepare you for the Multi-Step TAKS Prep on page 854. The figure sh... |
the reflections. Write the vector in component form. SPIRAL REVIEW Determine whether the set of ordered pairs represents a function. (Previous course) (-3, -1), (1, 2), (-3, 1), (5, 10) 30. ⎬ ⎨ (-6, -5), (-1, 0), (0, -5), (1, 0) 29. ⎬ ⎨ Find the length of each segment. (Lesson 11-6) 31. ̶̶ EJ 32. ̶̶ CD... |
854 854 Chapter 12 Extending Transformational Geometry ������������������������������������������ SECTION 12A Quiz for Lessons 12-1 Through 12-4 12-1 Reflections Tell whether each transformation appears to be a reflection. 1. 2. Copy each figure and the line of reflection. Draw the reflection of the figure across the ... |
of the figure such that the image coincides with the preimage. Line Symmetry A figure has line symmetry (or reflection symmetry) if it can be reflected across a line so that the image coincides with the preimage. The line of symmetry (also called the axis of symmetry) divides the figure into two congruent halves. E X ... |
plane can divide the figure into two congruent reflected halves. A three-dimensional figure has symmetry about an axis if there is a line about which the figure can be rotated (by an angle greater than 0° and less than 360°) so that the image coincides with the preimage. E X A M P L E 4 Identifying Symmetry in Three D... |
15 16–18 19 20–22 1 2 3 4 TEKS TEKS TAKS TAKS Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. Skills Practice p. S27 Application Practice p. S39 16. 17. 18. 12-5 Symmetry 859 859 ����������������� 19. Art Op art is a style of art that uses op... |
(3, -1) 33. Art The Chokwe people of Angola are known for their traditional sand designs. These complex drawings are traced out to illustrate stories that are told at evening gatherings. Classify the symmetry of the Chokwe design shown. Algebra Graph each function. Tell whether the graph has line symmetry and/or rotat... |
part of a shape with a center of rotation and a given rotational symmetry. Copy and complete each figure. 47. order 4 48. order 6 49. order 2 50. Write About It Explain the connection between the angle of rotational symmetry and the order of the rotational symmetry. That is, if you know one of these, explain how you c... |
-4) 67. Reflect point P across the line y = x and then translate it along the vector 〈2, -4〉. 68. Rotate point P by 90° about the origin and then reflect it across the y-axis. 69. Translate point P along the vector 〈1, 0〉 and then rotate it 180° about the origin. 862 862 Chapter 12 Extending Transformational Geometry 1... |
+ m∠2 + m∠3 = 180° m∠1 + m∠2 + m∠3 + m∠1 + m∠2 + m∠3 = 360° E X A M P L E 2 Using Transformations to Create Tessellations Copy the given figure and use it to create a tessellation. Step 1 Rotate the triangle 180° about the midpoint of one side. Step 2 Translate the resulting pair of triangles to make a row of triangle... |
tessellation. It is neither regular nor semiregular. Classify each tessellation as regular, semiregular, or neither. 3a. 3b. 3c. E X A M P L E 4 Determining Whether Polygons Will Tessellate Determine whether the given regular polygon(s) can be used to form a tessellation. If so, draw the tessellation. A B No; each ang... |
3 4 TEKS TEKS TAKS TAKS Skills Practice p. S27 Application Practice p. S39 PRACTICE AND PROBLEM SOLVING Interior Decorating Identify the symmetry in each wallpaper border. 15. 16. Copy the given figure and use it to create a tessellation. 18. 18. 19. 17. 20. Classify each tessellation as regular, semiregular, or neith... |
sphere using regular hexagons and regular pentagons. Can these two shapes be used to tessellate a plane? Explain your reasoning. 43. Chemistry A polymer is a substance made of repeating chemical units or molecules. The repeat unit is the smallest structure that can be repeated to create the chain. Draw the repeat unit... |
3, 4) and has center (0, 0) 57. ⊙T that passes through (1, -1) and has center (5, -3) Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. (Lesson 12-5) 58. 59. 60. 12-6 Tessellations 869 869 12-6 Use Transformations to Extend Tessellations In Les... |
properties and transformations.... Objective Identify and draw dilations. Vocabulary center of dilation enlargement reduction Also G.2.A, G.11.B, G.11.D Who uses this? Artists use dilations to turn sketches into large-scale paintings. (See Example 2.) Recall that a dilation is a transformation that changes the size of... |
A M P L E 2 Drawing Dilations Copy the triangle and the center of dilation P. Draw the image of △ABC under a dilation with a scale factor of 1 __. 2 Step 1 Draw a line through P and each vertex. Step 2 On each line, mark half the distance from P to the vertex. Step 3 Connect the vertices of the image. 2. Copy the figu... |
(-2 (-1), -2 (1) ) = A' (2, -2) B (-2, -1) → B' (-2 (-2), -2 (-1) ) = B' (4, 2) C (-1, -2) → C' (-2 (-1), -2 (-2) ) = C' (2, 4) Graph the preimage and image. 4. Draw the image of a parallelogram with vertices R (0, 0), S (4, 0), T (2, -2), and U (-2, -2) under a dilation centered at the origin with a scale factor of -... |
, B (2, 2), C (4, 0) ; scale factor: 2 10. J (-2, 2), K (4, 2), L (4, -2), M (-2, -2) ; scale factor: 1 _ 2 11. D (-3, 3), E (3, 6), F (3, 0) ; scale factor: - 1 _ 3 12. P (-2, 0), Q (-1, 0), R (0, -1), S (-3, -1) ; scale factor: -2 PRACTICE AND PROBLEM SOLVING Tell whether each transformation appears to be a dilation.... |
), F (-2, -4), G (-4, 0), H (-2, 4), J (2, 4) ; scale factor: - 1 _ 2 Each figure shows the preimage (blue) and image (red) under a dilation. Write a similarity statement based on the figure. 24. 25. 26. The rectangular prism shown is enlarged by a dilation with scale factor 4. Find the surface area and volume of the i... |
under a dilation centered at the origin with scale factor 2 followed by a reflection across the x-axis. b. Draw the image of △ABC under a reflection across the x-axis followed by a dilation centered at the origin with scale factor 2. c. Compare the results of parts a and b. Does the order of the transformations matter... |
that has a vertex at (0, -2)? - 1 _ 2 -1 -2 -4 47. Rectangle ABCD is enlarged under a dilation centered at the origin with scale factor 2.5. What is the perimeter of the image? 15 24 30 50 48. Gridded Response What is the scale factor of a dilation centered at the origin that maps the point (-2, 3) to the point (-8.4,... |
(-1, -4) Determine whether the polygons can be used to tessellate a plane. (Lesson 12-6) 55. a right triangle and a square 56. a regular nonagon and an equilateral triangle Using Technology Use a graphing calculator to complete the following. 1. △ABC with vertices A (3, 4), B (5, 2), and C (1, 1) can be represented ⎡ ... |
iz for Lessons 12-5 Through 12-7 12-5 Symmetry Explain whether each figure has line symmetry. If so, copy the figure and draw all lines of symmetry. 1. 2. 3. Explain whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. 4. 5. 6. 12-6 Tessellations Copy ... |
that is generated by iteration is called a fractal. E X A M P L E 1 Creating Fractals Continue the pattern to draw stages 3 and 4 of this fractal, which is called the Sierpinski triangle. To go from one stage to the next, remove an equilateral triangle from each remaining black triangle. Stage 0 Stage 1 Stage 2 Stage ... |
..................... 873 enlargement............................. 873 regular tessellation....................... 864 frieze pattern............................. 863 rotational symmetry...................... 857 glide reflection........................... 848 semiregular tessellation................... 864 glide refle... |
824–830) TEKS G.2.A, G.2.B, G.7.A, G.10.A E X A M P L E EXERCISES ■ Reflect the figure with the given vertices across the given line. A (1, -2), B (4, -3), C (3, 0) ; y = x To reflect across the line y = x, interchange the x- and y-coordinates of each point. The images of the vertices are A' (-2, 1), B' (-3, 4), and C... |
vertices along the given vector. 17. R (1, -1), S (1, -3), T (4, -3), U (4, -1) ; 〈-5, 2〉 18. A (-4, -1), B (-3, 2), C (-1, -2) ; 〈6, 0〉 19. M (1, 4), N (4, 4), P (3, 1) ; 〈-3, -3〉 20. D (3, 1), E (2, -2), F (3, -4), G (4, -2) ; 〈-6, 2〉 12-3 Rotations (pp. 839–845) TEKS G.2.A, G.2.B, G.7.A, G.10.A E X A M P L E EXERCI... |
EXERCISES ■ Draw the result of the composition of isometries. Translate △MNP along across line ℓ. v and then reflect it Draw the result of the composition of isometries. 29. Translate ABCD along v and then reflect it across line m. First draw △M'N'P', the translation image of △MNP. Then reflect △M'N'P' across line ℓ... |
essellation is semiregular. 42. 12-7 Dilations (pp. 872–879) TEKS G.2.A, G.11.A, G.11.B, G.11.D E X A M P L E EXERCISES ■ Draw the image of the figure with the given vertices under a dilation centered at the origin using the given scale factor. A (0, -2), B (2, -2), C (2, 0) ; scale factor: 2 Tell whether each transfor... |
line y = 4. Describe a single transformation that moves the rectangle from its starting position to its final position. 10. Tell whether the “no entry” sign has line symmetry. If so, copy the sign and draw all lines of symmetry. 11. Tell whether the “no entry” sign has rotational symmetry. If so, give the angle of rot... |
the x-axis, what is the resulting image? (A) (-5, -2) (B) (2, 5) (C) (2, -5) (D) (-2, 5) (E) (5, 2) 4. After a composition of transformations, the line segment from A (1, 4) to B (4, 2) maps to the line segment from C (-1, -2) to D (-4, -4). Which of the following describes the composition that is applied to ̶̶ AB to ... |
12, 0) and is then rotated about the origin by 15° every 0.005 second. Give the bird’s position after 0.015 second. Round the coordinates to the nearest tenth. (8.49, 8.49) (-12, 0) (0, 12) (-8.49, 8.49) What are you asked to find? the coordinates of the bird’s position after 0.015 seconds, to the nearest tenth What in... |
in the test item can you find the important information (data) needed to solve the problem? Make a list of this information. Item D Multiple Choice △ABC is reflected across the x-axis. Then its image is rotated 180° about the origin. What are the coordinates of the image of point B after the reflection? (-4, -1) (-1, ... |
two times the height of the cylinder. What is the volume of the cone? 8 cubic centimeters 12 cubic centimeters 16 cubic centimeters 48 cubic centimeters 8. What is the measure of ∠PRQ? Round to the nearest degree. 63° 127° 117° 45° 9. Which mapping represents a rotation of 270° about the origin? (x, y) → (-x, -y) (x, ... |
C (-7, y), D (1, -3), and E (-3, -2), what is the value of y if ̶̶ BD ǁ ̶̶ CE? -12 -8 3.5 8 Gridded Response 14. △ABC is a right triangle such that m∠B = 90°. If AC = 12 and BC = 9, what is the perimeter of △ABC? Round to the nearest tenth. 15. A blueprint for an office space uses a scale of 3 inches: 20 feet. What is... |
Isabel Lighthouse was built in 1853 on a prominent bluff on the mainland. Today, the fully restored lighthouse is the only one in Texas that is open for climbing and viewing. Port Isabel Port Isabel ge07ts_c12psl001a Choose one or more strategies to solve each problem. 1st pass 9/06/05 dtrevino 15 miles at sea. To the... |
Hondo Lift Bridge 10 ft 27 ft 138 ft 73 ft 2. It takes about 7 min to completely lift the roadbed of the Tule Lake Lift Bridge. At what speed, in feet per minute, does the lifting mechanism translate the roadbed? Round your answer to the nearest foot per minute. 3. To the nearest second, how long does it take the Tule... |
..................................... S42 Work Backward................................................. S43 Find a Pattern.................................................. S44 Make a Table................................................... S45 Solve a Simpler Problem........................................ S46 Use Lo... |
............................. S50 Properties..................................................... S51 Estimation, Rounding, and Reasonableness...................... S52 Classify Real Numbers........................................... S53 Exponents...................................................... S53 Properties of ... |
and Expressions....................................... S57 Solving Linear Equations....................................... S58 Solving Equations for a Variable.................................. S59 Writing and Graphing Inequalities............................... S59 S2S2 S2 Student Handbook Solving Linear Inequalities... |
................................................... S64 Quadratic Functions............................................ S65 Factoring to Solve Quadratic Equations........................... S66 The Quadratic Formula.......................................... S66 Solving Systems of Equations................................. |
........................... S72 Relative and Absolute Error..................................... S73 Significant Digits............................................... S73 Choose Appropriate Units....................................... S74 Nonstandard Units.............................................. S74 Use Tools for... |
............................... S79 Quartiles and Box-and-Whisker Plots............................. S80 Circle Graphs.................................................. S80 Misleading Graphs and Statistics................................ S81 Venn Diagrams................................................. S81 Postulates,... |
Draw and label each of the following. 7. a ray with endpoint A that passes through B 8. a line PQ that intersects plane D Lesson 1-2 Find each length. 9. MN 10. MO 11. Segments that have the same length are?. ̶̶̶̶ 12. Construct a segment congruent to AB. Then construct the midpoint M. 13. M is the midpoint of ̶̶ ... |
your answer to the nearest hundredth. 31. 33. 32. Lesson 1-6 34. The formula to find the midpoint M of ̶̶ AB with endpoints A ( x 1, y 1 ) and B ( x 2, y 2 ) is?. ̶̶̶̶ Find the coordinates of the midpoint of each segment. 35. ̶̶̶ WX with endpoints W (-4, 1) and X (2, 9) ̶̶ YZ with midpoints Y (4, 8) and Z (-1, -4) 36.... |
2 Find the next item in each pattern. 1. 3, 7, 11, 15, … 2. -3, 6, -12, 24, … 3. Complete the conjecture “The product of two negative numbers is?.” ̶̶̶̶ 4. Show that the conjecture “The quotient of two integers is an integer” is false by finding a counterexample. Identify the hypothesis and conclusion of each condition... |
sides have different lengths,” write the converse and a biconditional statement. 18. Determine if the biconditional “n + 3 = -1 ↔ n = -4” is true. If false, give a counterexample. Write each definition as a biconditional. 19. A parallelogram is a quadrilateral with two pairs of parallel sides. 20. Congruent angles hav... |
and ∠4 are supplementary. 3. ∠1 ≅ ∠4 4. m∠1 = m∠4 3. ≅ Supps. Thm. 4. Def. of ≅ 27. Use the given two-column proof to write a paragraph proof. Given: ∠1 ≅ ∠3 Prove: ∠4 ≅ ∠5 Proof: Statements Reasons 1. ∠1 ≅ ∠3 1. Given 2. ∠1 ≅ ∠4, ∠3 ≅ ∠5 2. Vert. Thm. 3. ∠1 ≅ ∠5 4. ∠4 ≅ ∠5 3. Trans. Prop. of ≅ 4. Trans. Prop. of ... |
������������������������� Lesson 3-4 18. Name the shortest segment from point A to BE. 19. Write and solve an inequality for x. Solve for x and y in each diagram. 20. 21. 22. Write a two-column proof. Given: ℓ ⊥ p, m ⊥ p Prove: ℓ ǁ m Lesson 3-5 Use the slope formula to determine the slope of each line. 23. FG ... |
S9S9 ���������������������������������������������������������������������� Chapter 4 Skills Practice Lesson Lesson Lesson 4-1 2-5 2-5 Lesson 4-2 Lesson 4-3 Classify each triangle by its angle measures. 1. △ABC 2. △BCD Classify each triangle by its side lengths. 3. △EFG 4. △FGH 5. △EFH 6. Find the side lengths of △JKL... |
-5 Determine if you can use ASA to prove the triangles congruent. Explain. 22. △ACB and △ACD 23. △EFG and △HGF Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know. 24. △ABC ≅ △EDC 25. △FGH ≅ △FJH Lesson 4-6 Lesson 4-7 26. Given: ̶̶̶ ̶̶ LP, MN ǁ ∠N... |
△YAZ is isosceles. TEKS TAKS Practice S11 S11 ������������������������������������������������������������������������������������������������������� Chapter 5 Skills Practice Lesson 5-1 Find each measure. 1. CD 2. HG 3. JM 4. m∠SRT, given m∠SRU = 126° 5. PQ 6. m∠WXV 7. Write an equation in point-slope form for the pe... |
��������������������������������������� Lesson 5-5 Write an indirect proof of each statement. 27. An isosceles triangle cannot have an obtuse base angle. 28. A right triangle cannot have three congruent sides. 29. Write the angles in order from smallest to largest. 30. Write the sides in order from shortest to longest.... |
whether it is concave or convex. 4. 5. 6. 7. Find the measure of each interior angle of pentagon ABCDE. 8. Find the sum of the interior angle measures of a convex heptagon. 9. Find the measure of each interior angle of a regular 15-gon. 10. Find the value of x in polygon FGHJKL. 11. Find the measure of each exterior a... |
, Q (1, -2), R (-2, 1) 30. S (-2, 7), T (2, 8), U (3, 4), V (-1, 3) 31. Given: WXYZ is a rectangle. Prove: ̶̶̶ WB ≅ ̶̶ YA ̶̶ XB ≅ ̶̶ AZ Lesson 6-5 Lesson 6-6 Determine if the conclusion is valid. If not, tell what additional information is needed to make it valid. ̶̶ ̶̶ 32. Given: XY ≅ XY ǁ ̶̶ XZ ⊥ Conclusion: WXYZ is ... |
���������������������������������������������������������� Chapter 7 Skills Practice Lesson 7-1 Write a ratio expressing the slope of each line. 1. line ℓ 2. line m 3. line n 4. The ratio of the side lengths of a quadrilateral is 2 : 4 : 5 : 6, and its perimeter is 85 inches. What is the length of the shortest side? 5.... |
: 1 ft 31. 1 cm : 10 ft 30. 1 cm : 5 ft 32. Given that △ABC ∼ △DEF, find the perimeter P and area A of △DEF. Lesson 7-6 33. Given that △RSV ∼ △RTU, find the coordinates of S and the scale factor. 34. Given: A (-3, 3), B (1, 7), C (5, 5), D (-1, 5), E (1, 4) Prove: △ABC ∼ △ADE TEKS TAKS Practice S17 S17 ���������������... |
, 1), F (2, 5) S18S18 TEKS TAKS Practice ��������������������������������������������������������������������������������������������������������� Lesson 8-4 Lesson 8-5 Classify each angle as an angle of elevation or angle of depression. 30. ∠1 31. ∠2 32. ∠3 33. ∠4 Use a calculator to find each trigonometric ratio. Rou... |
�������������������������������������������������������������� Chapter 9 Skills Practice Lesson 9-1 Find each measurement. 1. the area of the parallelogram 2. the perimeter of the rectangle in which A = 15 x 2 ft 2 3. b 2 of the trapezoid in which A = 35 ft 2 4. the area of the kite 5. the base of a triangle in which h... |
of each change on the area of the given figure. 24. The height of the rectangle with height 10 ft and width 12 ft is multiplied by 1 _. 2 25. The base of the parallelogram with vertices A (-2, 3), B (3, 3), C (0, -1), D (-5, -1) is doubled. Describe the effect of each change on the perimeter or circumference and the a... |
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