1. LT 7.5 Apply Properties of Similar Triangles

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

3. 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

4. Example 1
Find PN.

5. 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

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

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

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

9. 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.

10. Example 4
Find PS and SR.