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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.

Picture of Angle Bisector Theorem


Example 1
The picture below shows the proportion in action .
picture of angle bisector theorem formula

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.
Answer
angle bisector

How about side AB below? Is it an angle bisector?
angle bisector
Hint, please
AB is an angle bisector if it divides the triangle proportionally.
Answer
Practice Problems


Problem 1)
Use the angle bisector theorem to find the missing side length of the triangle below
Answer

Side Splitter Theorem Picture
Problem 2)
What is the length of XY in the triangle below?
Answer
angle bisector theorem problem