Points of Concurrency

Front

What is the centroid of a triangle?

Back

The centroid is the point of concurrency of the medians of a triangle. It is the center of mass and divides each median into a ratio of 2:1.

Front

What is the circumcenter of a triangle?

Back

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

Front

What is the incenter of a triangle?

Back

The incenter is the point of concurrency of the angle bisectors of a triangle. It is equidistant from all three sides.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point of concurrency of the altitudes of a triangle. Its position varies depending on the type of triangle (acute, right, obtuse).

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

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 a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.

Front

What is an angle bisector?

Back

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

Front

How many points of concurrency are there in a triangle?

Back

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

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.