Chapter 7.5, Problem 35HP

To determine

To compare and contrast: Theorem 7.9 and Angle Bisector Theorem.

Explanation of Solution

Theorem 7.9 is about two similar triangles and states that the corresponding angle bisectors of two similar triangles are proportional to the corresponding sides of the triangles.

For example:

  

  $\Delta QTS\sim \Delta XWZ$

As per Theorem 7.9:

  $\frac{TR}{WY}=\frac{QT}{XW}$

Angle Bisector Theorem is about one triangles and states that the segments of the side divided by the angle bisector from opposite vertex are proportional to the two other sides.

For example:

  

As per Angle Bisector Theorem:

  $\frac{YW}{WZ}=\frac{YX}{XW}$