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7-5: Parts of Similar Triangles

7-5: Parts of Similar Triangles. Expectations: G1.2.5: Solve multi-step problems and proofs about the properties of medians, altitudes and perpendicular bisectors to the sides of a triangle and the angle bisectors of a triangle.

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7-5: Parts of Similar Triangles

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  1. 7-5: Parts of Similar Triangles • Expectations: • G1.2.5: Solve multi-step problems and proofs about the properties of medians, altitudes and perpendicular bisectors to the sides of a triangle and the angle bisectors of a triangle. • G2.3.4: Use theorems about similar triangles to solve problems with and without the use of coordinates.

  2. Proportional Perimeters Theorem • If two triangles are similar, then the ratio of corresponding perimeters is equal to the ratio of corresponding sides.

  3. If F ~ G, then: G F z x a c y b a b c a + b + c = = = x y z x + y + z Proportional Perimeters Theorem

  4. If ABC ~ XYZ, AB = 15, XY = 25 and the perimeter of XYZ = 45, what is the perimeter of ABC?

  5. Corresponding Altitudes Theorem • If two triangles are similar, then the ratio of corresponding altitudes is equal to the ratio of corresponding sides.

  6. F G a c w y z d x b If F ~ G, then, a b c d = = = w x y z Corresponding Altitudes Theorem

  7. M x 10 K L 12.5 If CDE ~KLM, determine the value of x. M 16 8 K L

  8. Corresponding Angle Bisectors Theorem • If two triangles are similar, then the ratio of corresponding angle bisectors is equal to the ratio of corresponding sides.

  9. G F y x c b d z a If F ~ G, then, w a b c d = = = w x y z Corresponding Angle Bisectors Theorem

  10. F B 9 x H E 7 8 D 10.4 A G 13 C The triangles below are similar and AD and EH are angle bisectors. Determine the perimeter of ∆EHG.

  11. Corresponding Medians Theorem • If two triangles are similar, then the ratio of corresponding medians is equal to the ratio of corresponding sides.

  12. G F y x c b z d a w If F ~ G, then, a b c d = = = w x y z Corresponding Medians Theorem

  13. ∆ABC ~ ∆XYZ. If the perimeter of ∆XYZ is half as much as the perimeter of ∆ABC, and AD and XU are medians, determine the length of XU. X A 22 Z U Y C D B

  14. Angle Bisector Theorem • An angle bisector of a triangle separates the opposite side into segments that have the same ratio as the other two sides.

  15. C A B D If CD bisects ACB then, AC BC . = AD BD Angle Bisector Theorem

  16. C A B D Determine the value of x in the figure below. 24 x 14 12

  17. Assignment • pages 373 – 377, # 13 – 33 (odds), 43, 47-57 (all).

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