note your teacher will grade your response to the questions 13 through 15 to ensure you receive proper credit for your answer. What are the properties of the center of a triangle
The properties of the center of a triangle are as follows:
13. Centroid: The centroid is the point of concurrency of the medians of a triangle. It is the point where all three medians intersect. The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side. The centroid divides the triangle into three smaller triangles of equal area.
14. Circumcenter: The circumcenter is the point of concurrency of the three perpendicular bisectors of a triangle. It is equidistant from the three vertices of the triangle. The circumcenter is important because it is the center of the circumcircle, which is the circle passing through all three vertices of the triangle. The distance between the circumcenter and any vertex is equal to the radius of the circumcircle.
15. Incenter: The incenter is the point of concurrency of the three angle bisectors of a triangle. It is equidistant from the three sides of the triangle. The incenter is significant because it is the center of the incircle, which is the circle tangent to all three sides of the triangle. The distance from the incenter to any side of the triangle is equal to the radius of the incircle.