1. 6.5 Parts of Similar Triangles

2. Proportional Perimeters Theorem
If two Δs are similar, then the perimeters are proportional to the measures of the corresponding sides.

3. Example 1:
If ∆ABC~ ∆XYZ, find the perimeter of ∆XYZ.

4. Your Turn:
If ∆NOP ~ ∆XQR, find the perimeter of ∆NOP.

6. Review: Identify the segment

7. Special Segments of ~ Δs
In ~ Δs, corresponding…
altitudes
angle bisectors
medians
are proportional to sides.
**Perpendicular bisectors are not

8. Example 2:
If ∆QRS ~ ∆CAT, find x.

9. Your Turn:
If ∆TUV ~ ∆ABC, find x.

10. Example 3:
The drawing below illustrates two poles supported by wires. ∆ABC ~ ∆GED, F is the midpoint of AC and C is the midpoint of GD. Also, FG=GC=DC. Find the height of the pole EC.

11. Your Turn:
The drawing below illustrates the legs, AE and CG of a table. The top of the legs are fastened so that AC measures 12 inches while the bottom of the legs open such that GE measures 36 inches. If BD measures 7 inches, what is the height h of the table?
Answer: 28 in.

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

13. Example 4
Find x.

14. Assignment