Incenter of a Triangle Worksheet
Explore the properties and construction of the incenter of a triangle, including angle bisectors and inscribed circles, for Grade 10 geometry students.
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Incenter of a Triangle
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Read each question carefully and answer to the best of your ability. Show all your work for construction problems.
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 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. Consider a triangle ABC with angle bisectors AD, BE, and CF. If AD, BE, and CF intersect at point I, what is point I called? Explain its property related to the sides of the triangle.
6. Construct the incenter of the triangle below. Then, construct the inscribed circle.
7. The incenter of an obtuse triangle lies outside the triangle.
True
False
8. The incenter is always equidistant from the vertices of the triangle.
True
False