Incenter of a Triangle Worksheet
Explore the properties and construction of the incenter of a triangle, including its relationship to angle bisectors and inscribed circles, suitable for Grade 12 Geometry.
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Incenter of a Triangle Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. What is the incenter of a triangle?
The intersection of the medians.
The intersection of the altitudes.
The intersection of the angle bisectors.
The intersection of the perpendicular bisectors.
2. The incenter of a triangle is equidistant from which parts of the triangle?
The vertices.
The midpoints of the sides.
The sides.
The altitudes.
3. The incenter is the center of the circle of the triangle.
4. Every triangle has exactly one .
5. Construct the incenter of the triangle below by drawing the angle bisectors. Then, draw the inscribed circle.
6. The incenter always lies inside the triangle.
True
False
7. The incenter is equidistant from the vertices of the triangle.
True
False
8. In triangle ABC, the angle bisectors of angle A, angle B, and angle C intersect at point I (the incenter). If m∠BAC = 70° and m∠ABC = 50°, find m∠BIC.
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