Page 169 - IM_FL_Geometry_Print Sample

9.4 Three Triangles In One
Cool Down: 5 minutes
Student Task Statement
Triangle is shown with its incenter centered at and radius . The length of is length of is . The length of is .
1. What is the area of triangle ?
2. What is the area of triangle
3. What is the area of triangle
4. What is the area of triangle ?
Student Response
1. 9 square units. 2. 10 square units. 3. 17 square units. 4. 36 square units.
Student Lesson Summary
. The
? ?
We saw before that the incenter of a triangle is a point that is the same distance from all
3 sides of the triangle. We also saw that the distance between a point and a line is measured along a perpendicular path. We can draw each of those 3 perpendicular paths from the incenter to each of the 3 sides. Because all 3 paths have the same length we can think of them as radii of a circle centered at the incenter. Because each radius is perpendicular to a side, each side must be tangent to this circle which we call the incircle of the triangle.
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Teacher Guide