Centers of Triangles

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.

Tags

CCSS.HSG.C.A.3

Front

What is the Orthocenter of a triangle?

Back

The Orthocenter is the point where the altitudes of a triangle intersect. It can be located inside, outside, or on the triangle depending on the type of triangle.

Tags

CCSS.HSG.CO.C.10

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 known as the center of mass or balance point of the triangle.

Tags

CCSS.HSG.CO.C.10

Front

What are Medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Tags

CCSS.HSG.CO.C.10

Front

What are Altitudes in a triangle?

Back

Altitudes are perpendicular segments from a vertex to the line containing the opposite side.

Front

What are Angle Bisectors in a triangle?

Back

Angle Bisectors are segments that divide an angle into two equal angles.

Tags

CCSS.HSG.CO.C.9

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 the center of the circumcircle.

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 point where they intersect is the Incenter.

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 point where they intersect is the Orthocenter.

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 point where they intersect is the Centroid.

Tags

CCSS.HSG.CO.C.10