ANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1

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1 ANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1 N W A S Use the diagram to answer the following questions # Give two other names for. Sample answer: PN O D P d F a. Give two other names for plane. Sample answer plane SAN 3. Name three points that are collinear. Name four points that are coplanar. Sample answer: NWP 4. Classify the polygon by the number of sides. Tell whether it is convex or concave. Octagon Convex 5. Write three names for the angle. Y, LYT, TYL L T Y In the figure,,,, and. 6. Name a pair of complementary angles. PSO, RQD 7. Name a pair of supplementary angles. ZQR, TSO R Z Q S P 8. Name a pair of adjacent angles. ZQR, RQD PSO, TSO D T O 9.Point M is the midpoint of. Find BM. 4x x A M B 10. You are making a picture frame in shop class. Two pieces of wood are cut to form complementary angles so they fit together properly. One angle needs to be and the other angle needs to be. What is the measure of the larger angle? 51

2 11.Two angles form a linear pair. The measure of one angle is eight times the measure of the other angle. Find the measure of the larger angle The measure of an angle is nine times the measure of its complement. Find the measure of the larger angle Point B is between points A and D, and point C is between points B and D. Which are possible lengths of when,, and? 65 <x < The midpoint of is. One endpoint is. Find the coordinates of endpoint G. (-8, -10) 15. Find the area of the polygon with vertices,,, and Find the perimeter of the polygon with vertices,,, and In the diagram,. Find The midpoint of segment JK is M(6, 3). One endpoint is J (14,9). Find the coordinates of endpoint K. (-,-3) Chapter B (7x + 34) D C (9x + 46) A 19. Find the values of x and y. x= 8 y= 14 (5y + 68) (3x + 18) (5x + ) (3y + 96) 0. In the diagram, and. Which angle measures are possible? and 64

3 In the diagram, AB = CD, BC = 3, AC =, and BD =. Match the numbered equation or reason below with its corresponding letter (a - g) to show that AB =. E A 3 B C D E_1. Equation D_. Reason 3 F_3. Reason 5 A_4. Equation 6 B 5. Reason 9 G_6. Equation 10 Equation Reason 1.,, 1. Given, Segment Addition Postulate Addition Addition Simplify a. e. b. f. c. g. d. Segment Addition Postulate False_ 7. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the conditional statement. Then decide whether it is true or false. If an animal is a dog, then the animal is a golden retriever. True 8. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the converse. Then decide whether it is true or false. If an animal is a golden retriever, then the animal is a dog.

4 True 9. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the inverse. Then decide whether it is true or false. If an animal is not a dog, then the animal is not a golden retriever. False 30. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the contrapositive. Then decide whether it is true or false. If an animal is not a golden retriever, then the animal is not a dog. A_31. If and, then. a. Transitive Property of Angle Congruence b. Symmetric Property of Angle Congruence c. Reflexive Property of Angle Congruence B_3. State the postulate illustrated by the diagram. C 33. a. Plane Intersection Postulate c. Two Point Postulate b. Plane-Line Postulate d. Line-Point Postulate D 34. a. Two-Point Postulate c. Three Point Postulate b. Plane-Point Postulate d. Plane Intersection Postulate A_35. a. Two Point Postulate c. Three Point Postulate b. Line Intersection Postulate d. Line-Point Postulate D_36. a. Plane Intersection Postulate c. Plane-Point Postulate b. Plane-Line Postulate d. Line Intersection Postulate

5 a. Two Point Postulate c. Line-Point Postulate b. Plane-Line Postulate d. Line Intersection Postulate Identify the numbered statement or reason in the two-column proof. Given Prove STATEMENTS REASONS Given Transitive Property of Equality Subtraction Property of Equality B_37. What is Reason? a. Subtraction Property of Equality c. Reflexive Property of Equality b. Transitive Property of Equality d. Symmetric Property of Equality C 38. What is Reason 3? a. Definition of complementary angles c. Angle Addition Postulate b. Substitution Property of Equality d. Linear Pair Postulate _A 39. What is Statement 4? a. b. c. d. D 40. What is Reason 5? a. Addition Property of Equality c. Multiplication Property of Equality b. Angle Addition Postulate d. Substitution Property of Equality

6 CHAPTER In th36e diagram,. Find the value of y. 74 b ( y + 34) c 36 SKIP THIS QUESTION 4.Find the value of x that makes. a b (x + 5) c 55 d Write an equation of the line passing through the point that is parallel to the line. y= /3 x 10/3 44. Write an equation of the line passing through the point (9, 3) that is perpendicular to the line. y= 17/7 x 13/7 In the diagram, think of each segment in the figure as part of a line.

7 45. Name the line(s) through point D that appear parallel to. a. c. and b. d. 46. Name the line(s) through point B that appear skew to. a. c. b. and d. and 47. Name the line through point D that appears perpendicular to. a. c. b. d. 48. Classify the pair of numbered angles. Alternate Interior Angles 49. Classify the pair of numbered angles. Consecutive Interior Angles 50. Classify the pair of numbered angles. Corresponding Angles List all: 51. Corresponding angles: 3-5, -4, 6-8, Alternate Interior angles: 3-7, Alternate Exterior angles: -6, 1-5

8 54. Consecutive Interior angles: 7-8, Find the value of x Find the value of x that makes line s parallel to line t Find the distance from point P to QS Write an equation of the line passing through point P1, 4 that is parallel

9 to y 6x 8. y= - 6x Write an equation of the line passing through point P1, 3 perpendicular to y 4x 7. y= -1/4 x + 11/4 that is CHAPTER Graph with endpoints C( 8, ) and D( 5, 6) and its image after the composition. Translation: Translation: y 8 D ( 5, 6) 6 D'(, 5) 4 C ( 8, ) C' ( 5, 1) x 61. The logo for a business is moved across a page 6 units right and 6 units down. Next, it is moved units left and units up. Rewrite the composition as a single translation. (x+4, y-4)

10 6. Graph with points F( 3, 4) and G( 3, ) and its image after the reflection in the line. Image of F (4,3) and image of G (,3) 63. Describe the similarity transformation that maps to (dilations have a center at the origin). 1 y 8 4 T B A R x S C a. rotation 180 about the origin followed by a dilation with a scale factor of b. rotation 90 counterclockwise about the origin followed by a dilation with a scale factor of c. rotation 180 about the origin followed by a dilation with a scale factor of

11 d. rotation 90 counterclockwise about the origin followed by a dilation with a scale factor of 64. You are rotating a figure 15 from G to. Find the measure of the acute angle formed by intersecting lines so that G can be mapped to using two reflections Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. P a. 30; enlargement c. 30; reduction C P' 1 b. ; reduction 7 d. 7 ; enlargement CP = Graph with endpoints at and and its image after the composition. Translation: Rotation: 90 counterclockwise about the origin

12 y 4 S'' S 4 4 x T T'' In the diagram,, is reflected in line k, is reflected in line j, centimeters, and the distance from to line j is 1 centimeters. Which of the following statements are true? B A k A' j A'' a. The distance from A to line k is 3 centimeters. b. cm c. line j d. A rotation maps onto. B' B'' ABC 68. Graph with endpoints at and and its image after the composition. Rotation: 180 about the origin Reflection: in the line

13 y S'' S 4 T' T 4 4 x 4 T'' S' 69. How many lines of symmetry does the rhombus have? Chapter A ramp is designed with the profile of a right triangle. The measure of one acute angle is times the measure of the other acute angle. Find the measure of each acute angle Find. 11

14 Find the value of x. 13 A x C B Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use. 73. Yes AAS

15 74. No 75. Which reason is not necessary to explain how you can find the distance across the lake? a. ASA Congruence Theorem b. Right Angles Congruence Theorem c. SSS Congruence Theorem d. Corresponding parts of congruent triangles are congruent. e. Vertical Angles Congruence Theorem 76. Which reason is not used in a plan to prove that? a. ASA Congruence Theorem c. SSS Congruence Theorem b. Reflexive Property of Congruence d. Congruent Complements Theorem 77. Which reason is not used in a plan to prove that? a. HL Congruence Theorem c. Base Angles Theorem b. Reflexive Property of Congruence d. Corresponding parts of congruent triangles are congruent.

16 78. Which reason is not used in a plan to prove that? a. Corresponding parts of congruent triangles c. Congruent Complements Theorem are congruent. b. Reflexive Property of Congruence d. Alternate Interior Angles Theorem SKIP THIS QUESTION 79. In the diagram, passes through the center C of the circle and. Name two triangles that are congruent. a. c. b. d. not enough information Match the numbered statement below with its reason to prove that. B B 81.. A a. Third Angles Theorem b. Given c. All corresponding parts are congruent. d. Reflexive Property of Congruence

17 B D_ B C CHAPTER 6 In Exercises 87-90, find the indicated measure. Explain your reasoning. 87. AD GJ PQ m DGF 76 In Exercise 91, find the coordinates of the circumcenter of the triangle with the given vertices. (3,) 91. J6, 0, K0, 0, L 0, 4 In Exercise 9, P is the incenter of triangle QRS. Use the given information to find the indicated measure. 9. PJ 4x 8, PL x 7 Find PK. 1

18 In Exercises 93-94, point P is the centroid of triangle ABC. Use the given information to find the indicated measures. 93. BL CP 16 Find BP 8 and PL 4 Find PL 8 and CL 4 In Exercise 95, find the coordinates of the centroid of the triangle with the given vertices. 95. Q, 6, R4, 0, S10, 6 (4,4) In Exercises , use the graph of triangle ABC. 96. In triangle ABC. show that the midsegment ED is parallel to BC and that ED 1 BC. 1 4 The slope of ED 3, and the slope of BC ED , So, ED BC. BC , so ED 1 BC. 97.Find the coordinates of the endpoints of midsegment EF, which is opposite AC. E1, 4, F 4,1 98. Show that EF is parallel to AC and that EF 1 AC. The slope of EF , and the slope of AC So, EF AC.

19 EF , AC , so EF 1 AC. 99. State the coordinates of the endpoints of midsegment DF. D,1, F 4, Show that DF is parallel to AB and DF 1 AB. The slope of DF AB 3 1 4, so 1 1 0, and the slope of 4 1 DF AB. AB So, DF AB. DF 4, and In Exercises , use triangle QRS, where A, B, and C are the midpoints of the sides When AB 16, what is QS? When CA 3x 1 and SR 5x 4, what is CA? When QR 5x and CB x 5, what is AR? 1 In Exercises , list the angles of the given triangle from smallest to largest N,L,M F=D, E In Exercises , list the sides of the given triangle from shortest to longest

20 AB, AC, BC QP,PR,QR In Exercises , is it possible to construct a triangle with the given side lengths? Explain , 37, 53 No , 16, 8 Yes In Exercises , copy and complete the statement with,, or. Explain your reasoning AC > DF 111. HGI = IGJ 11. 1< 113. KL< MN