Centers of Triangles

Front

What is the circumcenter of a triangle?

Back

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

Front

What is the centroid of a triangle?

Back

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

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides 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. Its position varies depending on the type of triangle (acute, right, or 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 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 line that divides an angle into two equal angles.

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

How many centers can be found in a triangle?

Back

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

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.