Points of Concurrency

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.

Front

How is the length of segments from the centroid to the vertices related to the length of the medians?

Back

The length from the centroid to a vertex is two-thirds the length of the median from that vertex to the midpoint of the opposite side.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices.

Front

What is the relationship between the circumcenter and the circumcircle?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

What are altitudes in a triangle?

Back

Altitudes are segments drawn from a vertex of a triangle perpendicular to the opposite side.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of a triangle intersect. It is the center of the incircle, which is tangent to all three sides.

Front

What is the relationship between the incenter and the incircle?

Back

The incenter is the center of the incircle, which is the circle that is tangent to all three sides of the triangle.

Front

What is a median in a triangle?

Back

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

Front

How many points of concurrency are there in a triangle?

Back

There are four main points of concurrency in a triangle: the centroid, circumcenter, orthocenter, and incenter.