Short Answer
Note: Your teacher will grade your response to questions 13–15 to ensure you receive proper credit for your answer.
What are the properties of the incenter of a triangle?
The incenter of a triangle is the point where the angle bisectors of the triangle intersect. The properties of the incenter include:
1. The incenter is equidistant from all sides of the triangle. This means that the distances from the incenter to the three sides of the triangle are equal.
2. The incenter is the center of the triangle's incircle. The incircle is the largest circle that can fit inside the triangle and it is tangent to all three sides of the triangle.
3. The incenter is the intersection point of the angle bisectors of the triangle. This means that the angles formed by the lines connecting the incenter to the three vertices of the triangle are equal.
4. The incenter divides the triangle's angles into two equal parts. This means that the angles formed by connecting the incenter to the vertices of the triangle are equal to half of the original angles of the triangle.
5. The incenter has the property that the distance from the incenter to any side of the triangle is equal to the radius of the incircle.