Constructing Angle Bisectors

Author:
Bob Allen
An angle bisector is a ray that has its endpoint at the vertex of the angle and divcides the angle into two angles of equal measure. In this investigation, you'll investigate a special property of points on an angle bisector.
Please read the following instructions carefully. 1. Use the Ray tool to draw ray AB and ray AC. Remember to label your points. 2. Use the Angle Bisector Tool then click either the two rays or points C, A, B in that order. Or is it B, A, C? 3. Construct a point D on the angle bisector with the Point on Object tool. 4. Use the Distance or Length tool to measure from point D to ray AB. 5. Use the Distace or Length tool to measure from point D to ray AC.

To confirm that ray AD bisects angle BAC, measure angles BAD and DAC. (If the correct angle doesn't show up, reverse the order you're clicking the points.) Drag points A, B, and C to change angle BAC. How do the angle measures compare?

Drag point D and observe the distances from point D to the two sides of the angle. Write a conjecture about any point on the bisector of an angle. Hint: The if part should include point D and the angle bisector and the then part should include the measurements from D to the angle.

Did you actually read the instructions this time?

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