Lesson 6

In this lesson, students explore properties of angle bisectors. To build intuition, students first observe that pouring salt on a triangle forms ridges that meet at a peak, and the ridges appear to be angle bisectors. Students go on to prove that a point is on an angle bisector if and only if it is equidistant from the rays that form the angle. Then, they show that all 3 angle bisectors of a triangle meet at a single point, the incenter of the triangle. This will lead to constructing a triangle’s inscribed circle in a subsequent lesson.

Students create viable arguments (MP3) when they use what they know about triangle congruence to prove facts about angle bisectors.

If desired, prepare a plate, bottle, container of salt, and a triangle made out of cardboard for the salt demonstration in the warm-up. Alternatively, prepare a method to show the embedded video for this activity.

The activity Point and Angle includes a digital and print version of the launch. For the digital version, be prepared to display an applet for all to see.