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8.6 Proportions and Similar Triangles

8.6 Proportions and Similar Triangles. Triangle Proportionality Theorem. If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. If TU ll QS, then . R. U. T. >. S. >. Q. Given AB ll ED, find EA. C.

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8.6 Proportions and Similar Triangles

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  1. 8.6 Proportions and Similar Triangles

  2. Triangle Proportionality Theorem • If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. If TU ll QS, then R U T > S > Q

  3. Given AB ll ED, find EA C 8 12 D E > 4 A > B 8 EA = 4(12) 8 EA = 48 EA = 6

  4. Converse of the Triangle Proportionality Theorem

  5. Determining Parallels • Given the diagram, determine whether MN || GH. G 21 M 56 16 L 48 N H

  6. Proportionality Theorem • If three parallel lines intersect two transversals, then they divide the transversals proportionally. UW=VX WY XZ U W Y Z X V

  7. Using Proportionality Theorems

  8. Theorem 8.7 • If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. If CD bisects <ACB, Then AD=CA DB CB A D B C

  9. Using Proportionality Theorems

  10. Given CD=14, find DB. A 9 15 15 DB = 9(14) 15 DB = 126 DB = 8.4 B C D

  11. Solve 20 f 10 8

  12. Solve. 10 9 8 s

  13. x 12 20 22

  14. Find the value of JN. J N 18 L 16 M 3 K

  15. Find the value of the variable. 33 q 11 9

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