Triangle Angle Bisector Theorem

What is the Angle Bisector theorem?

Answer: As you can see in the picture below, the angle bisector theorem states that the angle bisector, like segment AD in the picture below, divides the sides of the a triangle proportionally.

The picture below shows the proportion in action.

Is side AB an angle Bisector?

Look at the measurements of the side lengths below to help you decide.

Hint, please

AB is an angle bisector if it divides the triangle proportionally.

Show Answer

AB is not an angle bisector because it does not create two proportional triangles.

$ \frac{14}{10} \color{Red}{ \ne} \frac{16}{12} $

How about side AB below? Is it an angle bisector?

Hint, please

AB is an angle bisector if it divides the triangle proportionally.

Show Answer

Yes, AB is n angle bisector because it divides the triangle proportionally.