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Proportional Segments Theorems in Triangles

Learn about the Proportional Segments Theorem in triangles, including examples and applications like parallel lines and angle bisectors. Solve problems to find unknown lengths and segments in various triangle scenarios.

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Proportional Segments Theorems in Triangles

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  1. Chapter 9 Section 9.8 Proportional Segments

  2. Triangle Proportional Thm. If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

  3. Example: Find x 4 cm 3 cm 2 cm x

  4. Corollary If 3 parallel lines are cut by two transversals then they divide the transversal proportionally

  5. Example: Find x a || b || c a 2 in b x 14 in c 12 in

  6. Example: Find Unknown Lengths 12 m 9 m x x + 1

  7. Example: Is KM || JN 1 1.5 K M 3 2 J N

  8. Example: Is QS || PT Q 2 3 P 4 S 7 T

  9. Triangle Angle Bisector Thm. If a ray bisects an angle of a triangle it divides the opposite side into proportional segments to the other 2 sides of the triangle.

  10. Example: Find t 6 ft 12 ft t 21 ft

  11. Example: Find x and y Perimeter: 40 ft 4 6 x y

  12. Homework WORKSHEET

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