Page 177 - IM_FL_Geometry_Print Sample

Student Response
In the acute triangle the circumcenter is located inside the triangle. In the right triangle, the circumcenter is located on the hypotenuse. In the obtuse triangle, the circumcenter is located outside the triangle.
Activity Synthesis
The important takeaway for discussion is that whether the circumcenter is inside, outside, or on the triangle depends on whether the triangle is acute, obtuse, or right, respectively. Examine the triangle whose circumcenter lies on one of the sides rst. Ask students,
• “What is the measure of the angle opposite the side with the circumcenter? How do you know?” (That angle measures radians because it is inscribed in a diameter that measures
radians, and an inscribed angle is half the measure of the central angles that trace out the same arc.) If not mentioned by students, suggest researching the relationship between inscribed angles and central angles in their reference charts.
Next, examine one angle of the triangle whose circumcenter lies inside the triangle. Ask students,
• “Does this angle trace out more than half the circle, or less than half the circle?” (The angle traces out less than half the circle.)
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Teacher Guide