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.
Lesson overview
 6.1 Warmup: Notice and Wonder: Salt Pile (5 minutes)

6.2 Activity: Point and Angle (15 minutes)
 There is a digital applet in this activity

6.3 Activity: What If There Are Three Sides? (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 6.4 Cooldown: Which is Which? (5 minutes)
Learning goals:
 Prove (using words and other representations) that the angle bisectors of a triangle are concurrent.
Learning goals (student facing):
 Let’s see what we can learn about a triangle by watching how salt piles up on it.
Learning targets (student facing):
 I can explain why the angle bisectors of a triangle meet at a single point.
 I know any point on an angle bisector is equidistant from the rays that form the angle.
Required preparation:
 If desired, prepare a plate, bottle, container of salt, and a triangle made out of cardboard for the salt demonstration in the warmup.
 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.
Glossary:
 incenter  The incenter of a triangle is the intersection of all three of the triangle’s angle bisectors. It is the center of the triangle’s inscribed circle.
 Access the complete Geometry Course Glossary.
Standards:
 This lesson builds on the standards:CCSS.HSGCO.C.10MS.GCO.10MO.G.CO.C.9CCSS.HSGCO.C.9MS.GCO.9MO.G.CO.C.8
 This lesson builds towards the standards:CCSS.HSGC.A.3MS.GC.3MO.G.C.A.3CCSS.HSGCO.C.10MS.GCO.10MO.G.CO.C.9CCSS.HSGCO.C.9MS.GCO.9MO.G.CO.C.8
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