Honors Geometry A. Semester Exam Review Answers

Transcription

1 Hnrs Gemetry A

2 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.

3 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

4 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

5 Unit 1, Tpic 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

6 Unit 1, Tpic 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 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, Given If tw parallel lines are cut by a transversal, then crrespnding angles are cngruent Vertical angles are cngruent Substitutin (statement int statement 3) r transitive prperty 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.

7 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 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 m The sum f three adjacent angles whse vertices lie n a line have a sum f m1m4 m3m5 3.If tw parallel lines are cut by a transversal, then the alternate interir angles have the same measure 4. m4 m m Substitutin (Statements 3 int statement )

8 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 DE 108 DE a. SAS similarity L L Crrespnding sides are prprtinal. Crrespnding angles are cngruent.

9 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 a. 1 1 :3 c. they are equal 48. a. see graph belw 1:3 c. n, rigid transfrmatins y preserve lengths A 5, a. The scale factr is 3 The center f dilatin is 5,8 O A C B4, 3-6 B -7 P C 7,6 x

10 50. a x x y y y 15 1y 15 y 7.5 y 51. a. 5 h h 80 m 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

11 AA Similarity c. SAS Similarity 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

12 54. All statements are true. 55. The triangles are cngruent. Hwever 16 1 sin A, sin B a. In 0 4 SQU,csS, In SRT,csS sinu 5 5 c. Yes. cs U , cst sin 0 16sin 0 V 16 V 5.47 ft V 58. a. 15 sin Yes, this is safe sin 70 L Lsin L sin 70 L 5.54 ft 4 L 70

13 59. a. cs15 580cs15 h 580 h 5100 ft h v 580 sin15 580sin15 v 580 v1367 ft v h a. c. x 15 0 x 65 x 5 5 y y 45 y 3600 y m The area f the leftmst triangle is m. The area f the middle triangle is m 0 tan 1, m Since m h 0 m x y 1 m 15 m Apprximately 1764 square meters (see wrk in bx). h sin 36.9, h 60sin m 60 m cs 36.9, m 60 cs m 60 Area f rightmst triangle is m

14 61. a A A A A ft 0 tan a. n n cs n 1.99 miles sin A mi mb 58 sin 58 sin 79 0 BC BC 3.15 ft