Centroids & Orthocenters in Triangles

Front

What is the centroid of a triangle?

Back

The centroid is the point of concurrency of the three medians of a triangle.

Tags

CCSS.HSG.CO.C.10

Front

If G is the centroid of triangle ABC and BE = 18, what is the length of BG?

Back

BG = 12 (The centroid divides each median in a 2:1 ratio).

Tags

CCSS.HSG.CO.C.10

Front

If DL = 24, what is the length of DG?

Back

DG = 8 (The centroid divides each median in a 2:1 ratio).

Tags

CCSS.HSG.CO.C.10

Front

How does the centroid divide each median?

Back

The centroid cuts each median into two segments, where the shorter segment is one third the length of the entire segment.

Tags

CCSS.HSG.CO.C.10

Front

What is a median in a triangle?

Back

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

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

Is segment AB a median, altitude, neither, or both?

Back

AB is an altitude.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the centroid and the medians of a triangle?

Back

The centroid is the point where all three medians intersect.

Tags

CCSS.HSG.CO.C.10

Front

What is the ratio in which the centroid divides each median?

Back

The centroid divides each median in a 2:1 ratio, with the longer segment being closer to the vertex.

Tags

CCSS.HSG.CO.C.10

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point of concurrency of the three altitudes of a triangle.

Tags

CCSS.HSG.C.A.3