IGD: Angle Bisector

Drag point A or B to change the size of the angle. Drag point O to move the entire construction.

The buttons for Steps 1‑5 construct the angle bisector. (Details about these steps are given in the Exploration section below.)

The Measure button can be used to verify that the angle bisector has been constructed.

Construct an angle bisector by following the steps outlined below. For each step, press the appropriate Step button.

1. Draw circle O.
2. Mark the points of intersection P and Q of this circle with the two sides of the angle.
3. Draw circles of the same radius with centers at P and Q. The radius must be long enough for the circles to intersect.
4. Mark a point of intersection D of the two circles that lies in the interior of the angle.
5. Draw ray OD. This ray is the angle bisector.

Click the Why It Works button, and then answer the following questions to prove that the construction forms an angle bisector.

• How are segments OP and OQ related? Explain.
• How are segments DP and DQ related? How do you know?
• What can you say about triangles ODP and ODQ? Why?
• What does this imply about ∠POD and ∠QOD?

What Are Some Properties and Applications of Angle Bisectors?

• See how to use angle bisectors to construct the incircle of a triangle.