Hnrs Gemetry A 015-016
Unit 1, Tpic 1 1. pint, line, and plane. angle bisectr cnstructin 3. Cnstruct segment BC, then cnstruct the perpendicular bisectr f CC. C B C 4. Draw a line thrugh pint H, then cpy the angle frmed s that its vertex is at pint H. 5. Each pint n the perpendicular bisectr is equidistant frm pints A and B. 6. Each pint n the angle bisectr is equidistant frm the sides f the angle. 7. Each crrespnding pair f pints are the same distance frm each ther.
Unit 1, Tpic 8. A 4, 9. A y C B E O C A x F B D a. A translatin five units t the right and three units dwn. xy, x5, y 3 c. Triangles that underg rigid transfrmatins preserve bth distance and angles, therefre the triangles are cngruent. d. See graph abve fr the transfrmed triangle. x, y x, y 10. a. x, y x, y c. x6, y d. y, x e. x, y f. yx, g. x, y h. x, y
11. a. y D C A B y 1 O A B x D C Yes, reflectin is a rigid transfrmatin, therefre lengths and angle measurements are preserved. c. Yes, it wuld be the same. 1. translatins, rtatins, and reflectins 13. cngruent 14. a. x-axis r the line x 180 degrees abut the pint,0 15. a. Yes, it is a reflectin. The image f pint x, y is x, y. N, it is nt a translatin. Pints A, B, and C d nt translate t pints A, B and C. c. Reflect acrss the y-axis, then reflect acrss the x-axis, then reflect acrss the y-axis OR reflect acrss the x-axis three cnsecutive times OR reflect acrss the x-axis, reflect acrss the y-axis, then reflect acrss the y-axis again. 16. a. y 3x y 3x c. y 3x 10
Unit 1, Tpic 3 17. AE BC FG 18. cngruent 19. RS TS, RW TU 0. RSW TSU, RS TS r W U, RU TU 1. RSW TSU, W U. RT, W U r R T, RSW TSU 3. N, since SSA is nt a cngruence therem. 4. The crrespnding 500 ft. sides are cngruent. The crrespnding 450 ft. sides are cngruent. The vertical angles included between the 500 ft. and 450 ft. sides are cngruent. Therefre the tw triangles are cngruent, and by CPCTC the ther crrespnding sides are cngruent, making the length f the pwer line 65 ft. 5. SAS 6. AAA cannt be used t prve tw triangles cngruent. 7. ASA 8. SSS 9. SSA cannt be used t prve triangles cngruent. 30. AAS
Unit 1, Tpic 4 31. Oppsite sides are parallel and cngruent. Diagnals bisect each ther. Oppsite angles are cngruent. Cnsecutive angles are supplementary. 3. Diagnals are cngruent. All angles are right angles. 33. All sides are cngruent. Oppsite angles are bisected by diagnals. Diagnals are perpendicular. 34. DF EF 35. EC 1, DE 11 36. a. AD BD AE EC c. DE is parallel t BC d. BC e. The rati AB : AD is :1 f. The rati AE : AC is 1: 37. a. Alternate interir, alternate exterir, crrespnding, and vertical linear pairs, same side interir, same side exterir 38. There are many different prfs. Belw is ne example. Statements Reasns 1. m n, 1 16 1. Given. 1 9. If tw parallel lines are cut by a transversal, then crrespnding angles are cngruent. 3. 9 1 3. Vertical angles are cngruent 4. 1 1 4. Substitutin (statement int statement 3) r transitive prperty 5. 16 1 5. Substitutin (statement 1 int statement 4) 6. p q 6. If tw lines are cut by a transversal s that crrespnding angles are cngruent, then the lines are parallel.
39. Statements Reasns 1. AC D, AB DE 1. Given. ACB DCE. Vertical angles are cngruent 3. ACB DCE 3. AAS 4. CE CB 4. CPCTC 40. Statements Reasns 1. C is the midpint f BE 1. Given. BC CE. Definitin f midpint 3. AB DC 3. Given 4. AB BE, DC BE 4. Given mbmdce 90 5. Definitin f perpendicular 5. BDCE 6. ABC DCE 6. SAS 7. A D 7. CPCTC 41. Given: m n Prve: m m4 m5 180 Statements Reasns 1. m n 1. Given. m1m m3 180. The sum f three adjacent angles whse vertices lie n a line have a sum f 180 3. m1m4 m3m5 3.If tw parallel lines are cut by a transversal, then the alternate interir angles have the same measure 4. m4 m m5 180 4. Substitutin (Statements 3 int statement )
Unit, Tpic 1 4. a. Statements Reasns 1. DE BC 1. Given ADE ABC. If parallel lines are cut by a transversal,. AED ACB then crrespnding angles are cngruent. 3. ADE ~ ABC 3. AA Similarity c. AD 8 9 EC Let AD x, then EC x Substituting: x 8 9 x x 7 x 36 x 6 AD 6 DE 15 18 15DE 108 DE 7. 43. a. SAS similarity 0 40 30 L L 60 44. Crrespnding sides are prprtinal. Crrespnding angles are cngruent.
45. a. Since QRS ~ QTU, then QRS T because crrespnding angles in similar triangles are cngruent. QRS and T are crrespnding angles f tw lines cut by a transversal. Since the crrespnding angles are cngruent, the lines are parallel. QR; TU 46. a. B parallel t c. 5 47. a. 1 1 :3 c. they are equal 48. a. see graph belw 1:3 c. n, rigid transfrmatins y preserve lengths A 5, 6 49. a. The scale factr is 3 The center f dilatin is 5,8 O 10 9 8 7 6 5 4 3 1-10 - 9-8 - 7-6 - 5-4 - 3 - - 1 1-1 3 4 5 6 7 8 9 10 A C - -3-4 -5 B4, 3-6 B -7 P -8-9 -10 C 7,6 x
50. a. 10 1 15 x x 18 10 1 y y 1.5 10y 15 1y 15 y 7.5 y 51. a. 5 h 9 144 h 80 m 144 80 7136 164.73 ft 5. Answers belw are examples. Yur numbers will be different. As lng as the angles are cngruent and sides prprtinal, then yur answer is crrect. a. SSS Similarity 6 8 9 1 1 18
AA Similarity 4 4 88 88 c. SAS Similarity 9 18 7 18 18 14 Unit, Tpic 53. a. BC AB c. d. e. f. g. h. BC AC AB AC BC AB AB AC BC AC AB BC i. A j. C k. AC
54. All statements are true. 55. The triangles are cngruent. Hwever 16 1 sin A, sin B. 0 0 56. a. In 0 4 SQU,csS, In 5 5 8 4 SRT,csS 10 5 0 4 sinu 5 5 c. Yes. cs U 15 3 6 3, cst 5 5 10 5 57. sin 0 16sin 0 V 16 V 5.47 ft V 58. a. 15 sin 17 61.9 Yes, this is safe. 15 17 4 sin 70 L Lsin 70 4 4 L sin 70 L 5.54 ft 4 L 70
59. a. cs15 580cs15 h 580 h 5100 ft h v 580 sin15 580sin15 v 580 v1367 ft v h 15 60. a. c. x 15 0 x 65 x 5 5 y 65 65 y 45 y 3600 y 60 65 m The area f the leftmst triangle is 1 15 0 150 m. The area f the middle triangle is 1 5 60 750 m 0 tan 1, m1 53.1 15 Since m 180 53.190 36.9 h 0 m x y 1 m 15 m Apprximately 1764 square meters (see wrk in bx). h sin 36.9, h 60sin 36.9 36 m 60 m cs 36.9, m 60 cs 36.9 48 m 60 Area f rightmst triangle is 1 36 48 864 m
61. a. 100 0 10000 400 A 10400 A A A 10400 10.0 ft 0 tan 100 11.3 6. a. n n 14 3 143cs 68 483.753 n 1.99 miles 63. 1 14 3sin 68 149.8 A mi mb 58 sin 58 sin 79 0 BC BC 3.15 ft