6.5 Parts of Similar Triangles

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

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

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

Review: Identify the segment

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

Example 2: If ∆QRS ~ ∆CAT, find x.

Your Turn: If ∆TUV ~ ∆ABC, find x.

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.

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.

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.

Example 4 Find x.

Assignment