Centers of Triangles

Front

What are the three main centers of a triangle?

Back

Centroid, Circumcenter, Incenter.

Front

What is the definition of the centroid of a triangle?

Back

The centroid is the point where the three medians of the triangle intersect.

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of the sides of the triangle intersect.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of the triangle intersect.

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is the relationship between the centroid and the medians of a triangle?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

What is an angle bisector in a triangle?

Back

An angle bisector is a line that divides an angle into two equal angles.

Front

What is the significance of the circumcenter in relation to the triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle, making it the center of the circumcircle.