LT 7.5 Apply Properties of Similar Triangles

Math Humor Q: What do you call two L’s?? A: A Parallel!!

Theorem 7-4-1: Triangle Proportionality Theorem If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally. Hypothesis A 𝐸𝐹 || 𝐵𝐶 E F Conclusion B C

Example 1 Find PN.

Theorem 7-4-2: Converse of the Triangle Proportionality Theorem If a line divides two sides of a triangle proportionally, then it is parallel to the third side. Hypothesis A E F Conclusion 𝐸𝐹 || 𝐵𝐶 B C

Example 2: AC = 36 cm, and BC = 27 cm. Verify that . 𝐷𝐸 || 𝐴𝐵

Corollary 7-4-3: Two – Transversal Proportionality If three or more parallel lines interest two transversals, then they divide the transversals proportionately.

Example 3: Use the diagram to find LM and MN to the nearest tenth.

Theorem 7-4-4: Triangle Angle Bisector Theorem An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides.

Example 4 Find PS and SR.