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Fun with Similar Triangles: Exploring Parallel Lines and Angle Similarity

Dive into the world of similar triangles through parallel lines and angle relationships. Understand patterns, solve for unknowns, and discover the beauty of geometric similarity.

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Fun with Similar Triangles: Exploring Parallel Lines and Angle Similarity

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  1. more fun with similar triangles Pamela Leutwyler

  2. AB is parallel to CD B A D C

  3.  ABC =  BCD AB is parallel to CD B A D C

  4.  ABC =  BCD  AEB =  CED AB is parallel to CD B  ABC =  BCD A E D C

  5.  ABC =  BCD AB is parallel to CD B  ABC =  BCD A  AEB =  CED E  BAE =  EDC D ABE is SIMILAR to CED C

  6. AB is parallel to CD B  ABC =  BCD  ABC =  BCD A  AEB =  CED x E  BAE =  EDC X D ABE is SIMILAR to CED C

  7. AB is parallel to CD B  ABC =  BCD  ABC =  BCD y A  AEB =  CED x E  BAE =  EDC X D Y ABE is SIMILAR to CED C

  8. AB is parallel to CD B  ABC =  BCD  ABC =  BCD y A z  AEB =  CED x E  BAE =  EDC X Z D Y ABE is SIMILAR to CED C

  9. AB is parallel to CD B  ABC =  BCD  ABC =  BCD y A z  AEB =  CED x E  BAE =  EDC X Z D Y = = C

  10. example 1

  11. these lines are parallel

  12. 10 feet 9 feet 7 feet x y 3 feet

  13. 10 feet 9 feet 7 feet x y 3 feet

  14. 10 feet 9 feet 7 feet x y 3 feet

  15. 10 feet 9 feet 7 feet x y 3 feet

  16. 10 feet 9 feet 7 feet x y = 2.7 3 feet = y = 2.7 feet

  17. 10 feet 9 feet 7 feet x= 2.1 y = 2.7 3 feet = x = 2.1

  18. 10 feet 9 feet 7 feet x= 2.1 y = 2.7 3 feet

  19. these lines are parallel

  20. these lines are parallel these angles have equal measure

  21. these lines are parallel these angles have equal measure these angles have equal measure

  22. these lines are parallel these angles have equal measure these angles have equal measure these triangles are similar

  23. Q P R = = q p these lines are parallel these angles have equal measure these angles have equal measure r these triangles are similar

  24. example 2

  25. BE is parallel to CD CD = 12 feet BE = 9 feet AD = 20 feet AE = ? C B D A E

  26. BE is parallel to CD CD = 12 feet BE = 9 feet AD = 20 feet AE = 15 feet = C B D A E x = 15

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