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Angles and Triangles Similar Triangles Assignment Test

Solve geometry problems involving similar triangles, angles, and side lengths. Find unknown lengths and angles based on given measurements and relationships in the figures.

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Angles and Triangles Similar Triangles Assignment Test

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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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