An email from a student

"I was just using your instructions to construct an angle bisector. How do you know that it really cuts the angle in half?"

Dear Student,
There are probably many ways to prove that the angle bisector that you have created is actually bisecting the angle. I can think of two very simple ways. Bisecting means to divide into two equal parts, so if you were to measure from the bisector to one of the angle's rays with your compass, and measured the other side in the exact same location they would have the same measure. Also, if you were to measure the angles of each "half" of your angle the angle measurements would be the same. Thank you for asking this great question!
Sincerly,
Madeleine G.