Geometry

Question Analysis

The main focus is to recall the definition of the centroid of a triangle, specifically identifying the type of line segments that intersect at the centroid.

Key Concept Explanation

Medians: A median of a triangle is a line segment that joins a vertex of the triangle to the mid - point of the opposite side. The centroid is defined as the point of concurrency of the three medians of a triangle.

Midsegments: A midsegment of a triangle is a line segment that connects the mid - points of two sides of a triangle. It is not related to the centroid.

Perpendicular Bisectors: The perpendicular bisectors of a triangle's sides are lines that are perpendicular to the sides and pass through their mid - points. The point of concurrency of perpendicular bisectors is the circumcenter, not the centroid.

Angle Bisectors: Angle bisectors of a triangle are lines that divide each angle of the triangle into two equal angles. The point of concurrency of angle bisectors is the incenter, not the centroid.

Step - by - Step Solution

1. Recall the definition of the centroid:

By definition, the centroid is the point where the three medians of a triangle meet.

So, the blank should be fille...