Page 165 - IM_FL_Geometry_Print Sample

2. Sample responses: Triangles and are congruent. Triangles and are congruent. Triangles and are congruent. The corresponding parts of these triangles are also congruent.
Activity Synthesis
Ask groups to share their responses. Here are some questions for discussion:
• “How are angle bisectors related to distances?” (Angle bisectors of the triangle are the sets of points that are the same distance from two sides of the triangle.)
• “Point is on all three angle bisectors at the same time. What does that mean in terms of distances?” (Point is the same distance away from the three sides of the triangle.)
9.2 The Circle Inside
15 minutes
In this activity, students create an arbitrary triangle and construct its incircle. Students use what they know about angle bisectors and constructions to nd the incenter. This activity goes a step further than the analysis of the incenter from the previous lesson by asking students to construct a circle centered at the incenter that is tangent to all three sides of a triangle. This special circle is called the incircle of the triangle.
Making dynamic geometry software available among tracing paper, straightedge, and compass gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Straightedge and compass constructions may take more time, but also might be more precise than folding tracing paper. If you are concerned with time, consider encouraging students to use paper folding. If students have access to dynamic geometry software, suggest that it might be a helpful tool in this activity.
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Teacher Guide