Unit 1, Tpic 1 1. pint, line, and plane 2. angle bisectr cnstructin 3. Cnstruct a perpendicular at pint B, then bisect the right angle that is frmed. B 45 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 DC and DE. 7. The lines never intersect. MCPS Answers Page 1
Unit 1, Tpic 2 8. A 4, 2 9. A y C F B E O C A B x 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. 3, 5 3,5 c. 4,3 d. 5,3 e. 3, 5 f. 5, 3 MCPS Answers Page 2
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. 12. translatins, rtatins, and reflectins 13. cngruent 14. a. x-axis r the line x 2 180 degrees abut the pint 2,0 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. MCPS Answers Page 3
Unit 1, Tpic 3 16. AE, BF, C G, DH AB EF, BC FG, CD GH, AD EH 17. cngruent 18. RS TS, RW TU 19. RSW TSU, RS TS r W U, RW TU 20. RSW TSU, W U 21. RT, W U r R T, RSW TSU 22. RW TU, RT r RSW TSU r RS TS, W U r R T 23. 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 by SAS, and by CPCTC the ther crrespnding sides are cngruent, making the length f the pwer line 625 ft. 24. SAS 25. AAA cannt be used t prve tw triangles cngruent. 26. ASA 27. SSS 28. SSA cannt be used t prve triangles cngruent. 29. AAS MCPS Answers Page 4
Unit 1, Tpic 4 30. Oppsite sides are parallel and cngruent. Diagnals bisect each ther. Oppsite angles are cngruent. Cnsecutive angles are supplementary. 31. Diagnals are cngruent. All angles are right angles. 32. All sides are cngruent. Oppsite angles are bisected by diagnals. Diagnals are perpendicular. 33. DF EF 34. x12, y 11, z 10 35. a. AD BD AE EC c. DE is parallel t BC d. AD BD e. AE EC f. BC 2 DE g. The rati AB : AD is 2:1 h. The rati AE: AC is 1:2 36. a. Alternate interir, alternate exterir, crrespnding, and vertical linear pairs, same side interir, same side exterir 37. There are many different prfs. Belw is ne example. Statements Reasns 1. m n, 1 16 1. Given 2. 1 9 2. If tw parallel lines are cut by a transversal, then crrespnding angles are cngruent. 3. 9 12 3. Vertical angles are cngruent 4. 1 12 4. Substitutin (statement 2 int statement 3) r transitive prperty 5. 16 12 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. MCPS Answers Page 5
38. Statements Reasns 1. AC D, AB DE 1. Given 2. ACB DCE 2. Vertical angles are cngruent 3. ACB DCE 3. AAS 4. CE CB 4. CPCTC 39. Statements Reasns 1. C is the midpint f BE 1. Given 2. BC CE 2. 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 Unit 2, Tpic 1 40. a. Statements Reasns 1. DE BC 1. Given ADE ABC 2. If parallel lines are cut by a transversal, 2. AED ACB then crrespnding angles are cngruent. 3. ADE ~ ABC 3. AA Similarity c. 15 x 9 12 x 20 9 y 24 30 y 11.25 MCPS Answers Page 6
41. a. SAS similarity 20 40 30 L L 60 42. a. Crrespnding sides are prprtinal. Crrespnding angles are cngruent. 43. 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 these crrespnding angles are cngruent, the lines are parallel. 44. a. B Q Q, QRS QTU, QSR QUT QR QS QR RT QR QS RS,, QT SU QS SU RT QU TU parallel t c. n the same line as d. 5 45. a. 1 1 2 3:2 c. they are equal MCPS Answers Page 7
46. a. A 5, 6 O -10-9 - 8-7 - 6-5 - 4-3 - 2-1 1 2 3 4 5 6 7 8 9 10-1 A C -2-3 -4 B4, 3-5 B -6 P -7-8 -9-10 y 10 9 8 7 6 5 4 3 2 1 C 7,6 x 1:3 c. they are equal 47. 10 12 15 x x 18 48. 301m xcm 100m 10cm x 30.1 49. a. 5 h 9 144 h 80 m 2 2 144 80 27136 164.73 ft MCPS Answers Page 8
50. 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 12 12 18 AA Similarity 42 42 88 88 c. SAS Similarity 9 128 7 18 128 14 MCPS Answers Page 9
Unit 2, Tpic 2 51. a. BC AB c. d. e. f. g. BC AC AB AC BC AB AB AC BC AC h. AB BC i. A j. C k. AC 52. All statements are true. 53. The triangles are cngruent. Hwever 16 12 sin A, sin B. 20 20 54. a. In 20 4 SQU,csS, In 25 5 8 4 SRT,csS 10 5 20 4 sinu 25 5 c. Yes. 15 3 6 3 cs U, cst 25 5 10 5 MCPS Answers Page 10
55. sin 20 16sin 20 V 16 V 5.47 ft V 56. a. 15 sin 17 61.9 Yes, this is safe. 15 17 sin 70 17sin 70 h 17 h h15.97 ft h 70 17 57. a. cs15 5280cs15 h 5280 h 5100 ft h v 5280 sin15 5280sin15 v 5280 v1367 ft v h 15 MCPS Answers Page 11
58. a. x 2 2 2 15 20 x 625 x 25 2 2 2 2 25 y 65 2 625 y 4225 y 3600 y 60 59. a. 2 2 2 100 20 10000 400 A 10400 A 2 A A 10400 102.0 ft 2 20 tan 100 11.3 MCPS Answers Page 12