3. Construct a perpendicular at point B, then bisect the right angle that is formed. 45 o

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1 Unit 1, Tpic 1 1. pint, line, and plane. angle bisectr cnstructin 3. Cnstruct a perpendicular at pint B, then bisect the right angle that is frmed. B 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. The lines never intersect. MCPS Answers Page 1

2 Unit 1, Tpic 1. A 4,. 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 3. a. x, y x, y c. x6, y d. y, x e. x, y f. yx, g. x, y h. x, y MCPS Answers Page

3 4. 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. 5. translatins, rtatins, and reflectins 6. cngruent 7. a. x-axis r the line x 180 degrees abut the pint,0 8. 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. 9. a. y 3x y 3x c. y 3x 10 MCPS Answers Page 3

4 Unit 1, Tpic 3 1. AE, BF, C G, DH AB EF, BC FG, CD GH, AD EH. cngruent 3. RS TS, RW TU 4. RSW TSU, RS TS r W U, RU TU 5. RSW TSU, W U 6. RT, W U r R T, RSW TSU 7. RW TU, RT r RST TSU r RS TS, W U r R T 8. 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. 9. SAS 10. AAA cannt be used t prve tw triangles cngruent. 11. ASA 1. SSS 13. SSA cannt be used t prve triangles cngruent. 14. AAS MCPS Answers Page 4

5 Unit 1, Tpic 4 1. Oppsite sides are parallel and cngruent. Diagnals bisect each ther. Oppsite angles are cngruent. Cnsecutive angles are supplementary.. Diagnals are cngruent. All angles are right angles. 3. All sides are cngruent. Oppsite angles are bisected by diagnals. Diagnals are perpendicular. 4. DF EF 5. EC 1, DE a. AD BD AE EC c. DE is parallel t BC d. AD BD e. AE EC f. BC DE g. The rati AB : AD is :1 h. The rati AE: AC is 1: 7. a. Alternate interir, alternate exterir, crrespnding, and vertical vertical, linear pairs 8. 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. MCPS Answers Page 5

6 9. 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 10. 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 11. 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 ) MCPS Answers Page 6

7 Unit, Tpic 1 1. 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 7.. a. SAS similarity L L Crrespnding sides are prprtinal. Crrespnding angles are cngruent. MCPS Answers Page 7

8 4. 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. 5. a. B Q Q, QRS QTU, QSR QUT QR QS QR RT QR QS RS,, RT SU QS SU RT QU TU parallel t c. n the same line as d a. 1 1 :3 c. they are equal 7. a. see graph belw 1:3 c. n, rigid transfrmatins y preserve lengths A 5, 6 O A C B4, 3-6 B -7 P MCPS Answers Page 8 C 7,6 x

9 8. a. The scale factr is 3 9. a. The center f dilatin is 5, x x y y y 15 1y 15 y 7.5 y 10. a. 5 h h 80 m ft 11. 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 MCPS Answers Page 9

10 AA Similarity c. SAS Similarity Unit, Tpic 1. 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 MCPS Answers Page 10

11 . All statements are true. 3. 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 6. a. 15 sin Yes, this is safe sin 70 L Lsin L sin 70 L 5.54 ft 4 L 70 MCPS Answers Page 11

12 7. 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 MCPS Answers Page 1

13 9. 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 MCPS Answers Page 13

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