Question

Is the centroid of a triangle equidistant from the three vertices?

Answer 1

Yes, the centroid of a triangle is equidistant from the three vertices.

Step-by-step explanation:

Yes, the centroid of a triangle is indeed equidistant from the three vertices.

The centroid of a triangle is the point where the three medians of the triangle intersect. A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Since the medians of a triangle intersect at the centroid, the distances from the centroid to each vertex along the medians are equal. This property can be proven using properties of similar triangles.

Answer 2

The point that is equidistant to all sides of a triangle is called the incenter.