Centroids

Front

What is a centroid in a triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

How do you find the length of a segment from a centroid to a vertex?

Back

The length from the centroid to a vertex is two-thirds the length of the median from that vertex to the midpoint of the opposite side.

Tags

CCSS.HSG.CO.C.10

Front

If the length of a median is 30, what is the length from the centroid to the vertex?

Back

20 (since the centroid divides the median in a 2:1 ratio).

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the segments created by the centroid on a median?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Tags

CCSS.HSG.CO.C.10

Front

If AZ = 24, what is AX if X is the centroid?

Back

AX = 16 (AX is two-thirds of AZ).

Tags

CCSS.HSG.C.A.3

Front

If ZX = 3, what is AZ if X is the centroid?

Back

AZ = 9 (AZ is twice ZX).

Tags

CCSS.HSG.CO.C.10

Front

What is the formula to find the length of a segment from the centroid to the midpoint of a side?

Back

The length is one-third of the median's length.

Tags

CCSS.HSG.CO.C.10

Front

If CP = 16, what is PL?

Back

PL = 8 (since the centroid divides the median in a 2:1 ratio).

Tags

CCSS.HSG.CO.C.10

Front

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

Back

BG = 12 (BG is two-thirds of BE).

Tags

CCSS.HSG.CO.C.10

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the balance point of the triangle, where it would balance if made of a uniform material.

Tags

CCSS.HSG.CO.C.10