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Use Proportionality Themes

Use Proportionality Themes. Ch 6.6. Triangle Proportionality Theorem. If a line parallel to one side of a triangle intersects the other 2 sides, then it divides the 2 sides proportionally. „ RQS ~ „RTU. Converse of the Triangle Proportionality Theorem.

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Use Proportionality Themes

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  1. Use Proportionality Themes Ch 6.6

  2. Triangle Proportionality Theorem • If a line parallel to one side of a triangle intersects the other 2 sides, then it divides the 2 sides proportionally. „RQS ~ „RTU

  3. Converse of the Triangle Proportionality Theorem • If a line divides 2 sides of a triangle proportionally, then it is parallel to the third side.

  4. Are the triangles similar? Can we find the length of QR? yes 6x = 36 x = 6

  5. Are the triangles similar? Can we find the length of all the sides? yes 360 = 24x x = 15

  6. Find the length of x that makes these 2 triangles similar. 96 = 6(x – 4) 96 = 6x -24 120 = 6x x = 20

  7. Find AB, FC, FE, and ED 8 7 6 10 12

  8. Page 400 # 3 - 7

  9. Theorem 6.6 • If 3 parallel lines intersect 2 transversals, then they divide the transversals proportionally.

  10. Theorem 6.7 • 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 2 sides.

  11. Find the length of HG 150x = 36000 x = 240

  12. Find the length of AB 8x = 60 x = 7.5

  13. Find the length of the missing side. 4a = 18 x = 4.5

  14. Find the length of the missing side. 3x = 28

  15. Find the length of the missing side. 12a = 72

  16. Find the length of the missing side 18 = 3x

  17. Find the length of the missing side 18x = 72

  18. Find the length of the missing side 3.5x = 27

  19. Worksheet

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