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A n g l e s

A n g l e s. a n d. T r i a n g l e s. 2 3. S i m i l a r T r i a n g l e s. A s s i g n m e n t T e s t. 1. 4. I n t h e fi g u r e , [ A D ] ∩ [C B ] = {E} , | A E | = 4 c m , | E B | = | E C | = 6 c m , | E D | = 9 c m , a n d | D C | = 8 c m. A D x 4 6 7 E 5 F B 15 2 C. B

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A n g l e s

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  1. Angles and Triangles 23 SimilarTriangles AssignmentTest 1. 4. Inthefigure, [AD]∩[CB]={E}, |AE|=4cm, |EB|=|EC|=6cm, |ED|=9cm,and |DC|=8cm. AD x4 6 7 E5F B 15 2C B x A 4 E 6 9 C 8 D 6 Inthefigure,m(AéBC)=m(DéFE). Whatis|ED|=xincm? Whatis|AB|=xincm? D B 2. Inthefigure, A 13x 17E 25 B1D9C ABCisatriangle, 5. Inthefigure, A 4 D 10 8x B6E10C |BD|=1cm, |AC|=10cm, |EC|=10cm, |AD|=4cm, |BD|=8cm, |BE|=6cm. |DC|=9cm, |EC|=5cm, |AE|=13cm,and FindthelengthofABincm. C Whatis|DE|=xincm? A)13 B)15 C)17 D)19 E)24 B A)4 B)5 C)6 D)7 E)8 3. Inthefigure, ABCandCDEaretriangles, A 7 8 6 5D 4 BxC 6. Inthefigure, AB 1510 E x9 CD [AB]//[CD], |AE|=15cm, |ED|=9cm, |BE|=10cm,and |EC|=x. ëA)=m(ëD), m( E |AB|=8cm, |AE|=7cm, |EC|=5cm, |ED|=6cm,and |CD|=4cm. Whatisthevalueofx? Whatis|BC|=xincm? C C A)8 B)7 C)6 D)5 E)4 A)15 B)12 C)10 D)9 E)6

  2. 23 AnglesandTriangles AssignmentTest 7. 10. Inthefigure, [AB]//[DC], Inthefigure, |AD|=4cm, |DB|=8cm, |BE|=12cm, |EC|=6cm,m(DéEB)=70°. A 1 D C 2 4 D 3 2 x 8 1 |AB|=2cm, |DB|=1cm,and 70° 6 B E C 12 A B 2 Whatisthemeasure degrees? of theangleACBin Whatis|BC|=xincm? A)50 B)55 C)60 D)65E)70 11. Inthefigure, [DE]//[BC], |DB|=6cm, |DE|=8cm,and |BC|=14cm. A 8. Inthefigure, [DE]//[BC], |AD|=8cm, |DB|=4cm,and |EC|=3cm. A x 8 x DE 8 6 DE 4 3 B C 14 Find|AD|=xincm. B C Whatis|AE|=xincm? A)6 B)7 C)8 D)9 E)12 A)9 B)8 C)7 D)6 E)4 12. Inthefigure, [DE]//[BC], [EF]//[CD], |BC|=8cm, |EF|=9cm,and |CD|=12cm. A 9. Inthefigure, ABCisatriangle, [DE]//[BC], |BD|=7cm, |AE|=6cm, |AD|=n,and |EC|=m. A D n 6 x B DE F E 9 8 7 m C D 12 B C Whatis|DE|=xincm? Whatisthevalueoftheproductm⋅n? A)42 B)36 C)28 D)21 E)14

  3. Angles and Triangles 24 SimilarTriangles AssignmentTest 1. 4. Inthefigure, [DE]//[AC], |BE|=8cm, |EC|=4cm, |DE|=6cm,and |AC|=x. Inthefigure, [AC]⊥[AB],[DE]⊥[AB], |EC|=5cm, |BE|=a, |AD|=a,and |BD|=x. A D x 6 B8E4C A a D x BaE5C Whatisxintermsofa? E Whatis|AC|=xincm? D A)15 B)12 C)10 D)9 E)8 2. Inthefigure, A x+1 D x–2 Bx+5ExC 5. A x DE 4 B12C [DE]//[AB], |BE|=x+5, |EC|=x, |DC|=x–2, |AD|=x+1. Inthefigure,ABCisatriangle,[CD]isanangle bisector,[DE]//[BC],|BC|=12cm,and|EC|=4cm. Whatis|AE|=xincm? Whatisxincm? E A)1 B)2 C)3 D)4 E)5 E A)8 B)6 C)4 D)3 E)2 6. Inthefigure, ABCisatriangle, [DE]//[BC], 7⋅|DE|=3⋅|BC|, |AD|=n,and |DB|=m. A n DE m BC 3. Inthefigure, A 3 K 4 F 2 x E D [KF]//[AC], m(BéFE)=90°, B C m(BéCD)=90°, |BK|=4cm, |AK|=3cm, and |FE|=2cm. Whatisthevalueoftheratio ? E Find|CD|=xincm. B A)3 B)3,5 C)4 D)4,5 E)5

  4. AssignmentTest24 AnglesandTriangles 7. 10. Inthefigure, ABCisatriangle, [DE]//[BC], |DE|=x–3, |BC|=2x+4,and |BD|=2⋅|AD|. Inthefigure, m(BéAC)=m(BéDE), |BD|=x+1, |BE|=2x–1, |DA|=2cm,and |EC|=3cm. A A 2 D D E x–3 x+1 2x–1 B E 3 C B C 2x+4 WhatisthelengthofBEincm? FindthelengthofDEincm. A)6 B)7 C)8 D)9 E)10 A)7 B)8 C)9 D)10 E)13 11. Inthefigure, ABCisanequilateral triangle, m(DéBA)=15°, |BD|=8ñ6cm,[DE]⊥[BC], [FH]⊥[BC],and C|DF|=|FC|. A 8. Inthefigure, [AD]//[EF], [FH]//[BC], |AD|=6cm, |EF|=4cm,and |FH|=5cm. D 6 D A F E 4 8S6 15° 5 H F x B E H Whatis|HC|=xin? x C B A)1 B)2 C)3 D)4 E)5 Whatis|BC|=xincm? A)15 B)12 C)10 D)9 E)8 12. Inthefigure, ABCisarighttriangle, BDEFisasquare, |AB|=4cm,and |BC|=3cm. A 9. Inthefigure, ABCisatriangle, [DE]//[BC], [FE]//[DC], |AE|=10cm, |EC|=5cm, |AF|=8cm,and |DB|=x A 8 10 E F F D E x B D C 5 B C Whatisthelengthofonesideofthesquare? Whatisthevalueofx? A)6 B)5 C)4 D)3 E)2

  5. Angles and Triangles 25 SimilarTriangles AssignmentTest 1. 4. Inthefigure, D 60° 46 50°60°70° BCEF A 13 12 D 4m BnE6C ABCisatriangle, m(BéAC)=m(DéEC), |AB|=12cm, |AD|=13cm, |EC|=6cm,and |DE|=4cm. A Inthefigure,m(ëB)=50°,m(ëC)=60°,m(ëD)=60°, m(ëE)=70°,|AC|=4cm,and|DE|=6cm. Whatisthescalefactorofsimilarity? Whatisthevalueoftheratio ? A B 5. A 10 D 4x B8C 2. Inthefigure, A 5 D7 9 E x BC ABCisatriangle, m(AéBC)=m(DéEA),), |AD|=5cm, |DB|=9cm,and |AE|=7cm. Inthefigure,m(BéAC)=m(BéCD),|AC|=10cm, |BC|=8cm,|BD|=4cm,and|DC|=x. Whatis|EC|=xin cm? Find|DC|=xincm? C B A)1 B)2 C)3 D)4 E)5 A)6 B)5 C)4 D)3 E)2 6. 3. EA 6x9 B10CD A x D 5 B12E3C Inthefigure,ABCisatriangle,m(BéAC)=m(DéEC), |BE|=12cm,|EC|=3cm,and|DC|=5cm. Inthefigure,[AB]⊥[AC],[AC]⊥[CE],[ED]⊥[BD], |AC|=6cm,|BC|=10cm,and|DE|=9cm. Whatis|CE|=xincm? Whatis|AD|=xincm? C B A)2 B)3 C)4 D)5 E)6 A)17 B)15 C)13 D)12 E)10

  6. AssignmentTest25 AnglesandTriangles 7. 10. Inthefigure, m(BAéC)=m(DBé |AB|=4cm, Inthefigure, ABCisatriangle, m(BéAC)=m(DéEC), |AB|=10cm, |DE|=5cm, |BE|=8cm, A A C), x D D 4 10 3 |BD|=3cm,and |BC|=8cm. x 5 6 C B 8 B 8 C E |DC|=6cm. Whatis|DC|=xincm? Whatis|AD|=xincm? A)3 B)4 C)5 D)6 E)8 A)1 B)2 C)3 D)4 E)5 8. Inthefigure, ABCisaright triangle, [AB]⊥[AC], [DH]⊥[BC], |AD|=2cm, |DC|=10cm, |DH|=8cm. 11. Inthefigure, ABCisaright triangle, m(AéBC)=m(DéAC), |BD|=5cm, |DC|=4cm,and |AC|=x. A A 2 D x 10 8 B H C 4 B D C 5 Whatis|AC|=xincm? Whatis|BH|incm? A)10 B)9 C)8 D)6 E)4 A)20 B)18 C)16 D)15 E)14 9. Inthefigure, [AB]⊥[BC], [AB]⊥[AD],[DE]⊥[AC], |AB|=12cm, |BC|=9cm, |AD|=6cm,and |DE|=x. A 6 D 12. Inthefigure, D A x E ABCisatriangle, [AD]//[BC], [AB]//[DE], |DE|=6cm,and |AE|=|EC|=5cm. 5 6 12 x E 5 B C 9 C B Whatis|DE|=xincm? Whatisthevalueofx? A)12 B)13 C)14 D)16 E)18

  7. Angles and Triangles 26 SimilarTriangles AssignmentTest 1. 4. Inthefigure, [DC]//[EF]//[AB], |AB|=18cm, |EF|=6cm,and |DC|=x. Inthefigure, A D xF 3 B4E6C DxC E6F A18B ABCisatriangle, |AB|=|AC|, m(BéDE)=m(FéEC), |BE|=4cm, |EC|=6cm,and |FC|=3cm. Whatis|DB|=xincm? Whatis|DC|=xincm? C B A)4 B)6 C)8 D)10 E)12 A)8 B)9 C)10 D)12 E)15 5. Inthefigure, ABCisa triangle, |AD|=|DB|, |BE|=|EC|, |DK|=2⋅|KC|, |FC|=4cm. A x D FK 4 BEC 2. Inthefigure, [DH]⊥[BC], [AB]⊥[AC], |HB|=|HC|, |AD|=3cm, |BD|=5cm. A 3 D 5 BH C Whatis|BH|incm? Whatis|AF|=xincm? C D C)2ñ5 E)4ñ2 A)8 B)9 C)10 D)12 E)16 A)3 B)4 D)5 6. Inthefigure, ABCisa triangle, [DE]//[BC], |AD|=6cm, |DB|=4cm, |FC|=8cm. A 6 DE x 4F 8 BC 3. Inthefigure, [AC]⊥[BE],[AB]⊥[ED], |AD|=2cm, |BC|=3cm, |CE|=5cm, |BD|=x. A 2 D F x B3C5E Whatis|BD|=xincm? Whatis|DF|=xincm? C E A)6 B)5 C)4 D)3 E)2 A)2,8 B)3,2 C)3,6 D)4,2 E)4,8

  8. AssignmentTest26 Inthefigure, [DC]//[EF]//[AB], |DE|=10cm, |EA|=12cm, |FB|=9cm,and |CF|=x. AnglesandTriangles 7. 10. Inthefigure, [DB]isanangle bisector, A D C 10 x 6 m(DéBA)=m(BéCD), |AD|=6cm,and |BD|=8cm. E F 8 D B 12 9 x A B C Whatis|CF|=xincm? Whatis|CD|=xincm? 11. Inthefigure, [FK]//[DE]//[BC], |AF|=3cm, |FD|=4cm, |DB|=6cm, |AK|=a,and |KE|=2a–1. A 8. Inthefigure, d1//d2//d3, |AB|=6cm, |BC|=8cm,and |DE|=4cm. 3 a A D d1 FK 4 E 6 B 4 2a–1 d 2 D E x F 8 C 6 x d 3 B C Whatis|EF|=xincm? Whatis|EC|=xincm? A)3 B)4 C)5 D)6 E)7 9. 12. Inthefigure, [AD]//[BE]//[CF], |DE|=2x, |EF|=3x+1, |AB|=x,and |BC|=4x. Inthefigure, D F 3x+1 E [AD]⊥[AB], [AB]⊥[BC],[AB]⊥[EF], |AD|=9cm, |BC|=6cm, |AF|=12cm 2x D C 9 E 6 x C 4x A B x A 12 F B Whatis|AB|=xincm? Whatis|FB|=xincm? A)12 B)10 C)9 D)8 E)6

  9. AnglesandTriangles 27 SimilarTriangles AssignmentTest 1. 4. DC x E 4 F 5 ABK C D E6 AFB 4 x Inthefigure,[AD]//[EF]//[BC],|AD|=4cm,and |BC|=6cm. Inthefigure,ABCDisaparallelogram,D,E,F,Kand A,E,Carecollinearpoints,|EF|=4cm,|FK|=5cm. Whatis|EF|=xincm? Whatis|DE|=xincm? B C A)2 B)2,4 C)3 D)3,6 E)4 A)9 B)8 C)6 D)5 E)4 5. Inthefigure, ABCisatriangle, [DE]//[BC], 2. A DE BC Inthefigure, ABCDisa parallelogram,A,E,F,K K x DF 2 E 4 AB andB,C,K collinearpoints, |AE|=4cm,and |EF|=2cm. are C A(ADE)=12cm2. WhatistheareaofthetriangleABCincm2? Whatis|FK|=xincm? B A A)18 B)27 C)36 D)45 E)54 A)6 B)5 C)4 D)3 E)2 6. Inthefigure, |BD|=|DC|, |AE|=4cm, |AF|=6cm, |FC|=9cm,and |EB|=x. A 46 EF K x9 BDC 3. Inthefigure, ABCisatriangle, [DE]//[AC], |BE|=4cm, |EC|=6cm,A(DECA)=42cm2 A D B4E6C WhatistheareaofthetriangleBEDincm2? Whatis|EB|=xincm? A C A)8 B)12 C)16 D)20 E)21 A)4 B)5 C)6 D)8 E)9

  10. AssignmentTest27 Inthefigure, |AF|=9cm, AnglesandTriangles 7. 10. A A 4 x |FB|=6cm, |AE|=4cm, |EC|=8cm,and |BD|=3cm. 9 E E F 8 F 8 6 K B D C x B3 D C Inthefigure,ABCisatriangle,[AD]isamedian, |AF|=|FD|,|EC|=8cm,and|AE|=x. Whatis|DC|=xincm? A)6 B)7 C)8 D)9 E)12 Whatis|AE|=xincm? A)6 B)5 C)4 D)3 E)2 11. Inthefigure, ABEandADCare triangles, AE|=5cm, |AD|=6cm, |EC|=6cm, |DB|=9cm, |DF|=3cm,and |FC|=x. A 8. Inthefigure, |BF|=|FA|, |BC|=2cm, |AE|=2cm,and |EC|=1cm. 6 5 A E D 3 2 F 6 F x 9 E 1 C x D C 2 B B Whatis|CD|=xincm? Whatis|FC|=xincm? A)4 B)5 C)6 D)8 E)9 12. Inthefigure, ABCisatriangle, |BD|=6cm, |DC|=8cm, |CE|=4cm,and |AE|=5cm. 9. A Inthefigure, ABCisatriangle, D,B,CandD,E,F arecollinearpoints, |AE|=8cm, |EB|=4cm, |DB|=4cm, |BC|=6cm,and |FC|=5cm. A 5 x 8 E F 4 F E 5 8 6 D C B 4 Whatisthevalueoftheratio ? D4B C 6 Whatis|AF|=xincm? A)2 B)3 C)4 D)5 E)6

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