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

Tags

CCSS.HSG.CO.C.10

Front

What segments intersect at the centroid?

Back

The medians of the triangle.

Tags

CCSS.HSG.CO.C.10

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 the center of the triangle's incircle.

Tags

CCSS.HSG.C.A.3

Front

What segments intersect at the incenter?

Back

The angle bisectors 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 three altitudes of a triangle intersect.

Tags

CCSS.HSG.CO.C.10

Front

What segments intersect at the orthocenter?

Back

The altitudes of the triangle.

Tags

CCSS.HSG.CO.C.10

Front

If AP = 12 in triangle ABC, what is AL if A is the centroid?

Back

AL = 18 (since the centroid divides each median in a 2:1 ratio).

Tags

CCSS.HSG.CO.C.10

Front

What is the circumcenter of a triangle?

Back

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

Tags

CCSS.HSG.C.A.3

Front

What segments intersect at the circumcenter?

Back

The perpendicular bisectors of the sides of the triangle.

Tags

CCSS.HSG.C.A.3

Front

How do you find the centroid of a triangle given its vertices?

Back

The centroid can be found by averaging the x-coordinates and y-coordinates of the vertices: (x1+x2+x3)/3, (y1+y2+y3)/3.

Tags

CCSS.HSG.C.A.3