1. Proportional Parts of a Triangle Proportional Perimeters Theorem If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides. Theorem 6.8 If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides.

2. Proportional Parts of a Triangle Theorem 6.9 If two triangles are similar, then the measures of the corresponding angle bisectors are proportional to the measures of the corresponding sides. Theorem 6.10 If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides.

3. Proportional Parts of a Triangle Triangle Angle-Bisector Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides of the triangle.

4. Example 5-1c If and RX = 20, find the perimeter of Answer: R

5. Example 5-2b Answer: and Find the ratio of the length of a median of to the length of a median of

6. Example 5-3c Answer: 17.5 N In the figure, is an angle bisector of and is an angle bisector of Find x if and

7. Example 5-4d The drawing below illustrates the legs, 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.