Similarity of Angle Bisectors in Triangles

Similarity of Angle Bisectors in Triangles

How to solve the similarity of angle bisectors in triangles problems: definition, example, and its solution.

Definition

The angle bisector of a triangle is a line segment that starts from the vertex and bisects the angle of the vertex.

The angle bisector of a triangle is a line segment
that starts from the vertex
and bisects the angle of the vertex.

Example

If triangle ABC ~ triangle A'B'C', find the value of x. The measure of the side of the left triangle: 10. The measure of the angle bisector of the left triangle: 9. The measure of the side of the right triangle: 7. The measure of the angle bisector of the right triangle: x.

If two triangles are similar,
then their angle bisectors are proportional.

So the angle bisectors and the sides are proportional:
9 / x = 10 / 7.