In this lesson, students apply what they’ve learned about angle bisectors to construct a triangle’s inscribed circle. Then, students use their knowledge of circumcenters and incenters to prove a property of equilateral triangles.
Students use appropriate tools like tracing paper, straightedge, compass, or dynamic geometry software strategically (MP5) when they construct the inscribed circle of an arbitrary triangle. They have an opportunity to construct a viable argument (MP3) when they write a proof that for an equilateral triangle, the incenter and circumcenter coincide.
Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Lesson overview
 7.1 Warmup: The Largest Circle (5 minutes)
 7.2 Activity: The Inner Circle (15 minutes)

7.3 Activity: Equilateral Centers (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 7.4 Cooldown: Circular Table Top (5 minutes)
Learning goals:
 Construct the inscribed circle of a triangle.
Learning goals (student facing):
 Let’s construct the largest possible circle inside of a triangle.
Learning targets (student facing):
 I can construct the inscribed circle of a triangle.
Required materials:
 Geometry toolkits
Standards:
 This lesson builds on the standards: CCSS.HSGC.A.3MS.GC.3CCSS.HSGCO.C.10MS.GCO.10MO.G.C.A.3MO.G.CO.C.9
 This lesson builds towards the standard: CCSS.HSGC.A.3MS.GC.3MO.G.C.A.3
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