Angle Bisectors of a Triangle

Intermediate Construction 5

We will now construct the last line of concurrency, the angle bisector. Use the angle bisector tool Toolbar Image to construct the three angle bisectors in the triangle below. Use the video if you get stuck but try to complete this on your own.

Think about it!

What do you notice about the three angle bisectors? What happens when you manipulate the triangle so it is acute? Right? Obtuse? Construct a perpendicular to one of the sides through the point you created with the angle bisectors then draw a circle with center at the intersection of the angle bisectors and edge at the place where the new perpendicular line intersects the side. What do you notice?