Centers of Triangles

Front

What is an altitude in a triangle?

Back

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

Front

What is the circumcenter of a triangle?

Back

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

Tags

CCSS.HSG.C.A.3

Front

What is the orthocenter of a triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

What is the incenter of a triangle?

Back

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

Tags

CCSS.HSG.C.A.3

Front

What is the centroid of a triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

What is a median in a triangle?

Back

A median is a line segment from a vertex to the midpoint of the opposite side.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The intersection point is the circumcenter.

Tags

CCSS.HSG.C.A.3

Front

How do you find the orthocenter of a triangle?

Back

To find the orthocenter, construct the altitudes from each vertex to the opposite side. The intersection point is the orthocenter.

Tags

CCSS.HSG.C.A.3

Front

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of each angle of the triangle. The intersection point is the incenter.

Tags

CCSS.HSG.C.A.3

Front

How do you find the centroid of a triangle?

Back

To find the centroid, draw the medians from each vertex to the midpoint of the opposite side. The intersection point is the centroid.

Tags

CCSS.HSG.CO.C.10