Centers of Triangles

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

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 circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of the sides of a triangle intersect. It is also the center of the circumcircle.

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 also the center of the incircle.

Front

Define 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

Define 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 the relationship between the centroid and the medians of a triangle?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

How many centers can be found in a triangle?

Back

There are four main centers in a triangle: centroid, orthocenter, circumcenter, and incenter.

Front

What is the significance of the circumcenter?

Back

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