Geometry Chapter 5 5-3 Medians and Centroids

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 the center of mass of the triangle.

Front

How does the centroid divide each median?

Back

The centroid divides each median into two segments, with the shorter segment being one third the length of the entire median.

Front

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

Back

20 units (two thirds of the median).

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.

Front

If G is the centroid of triangle ABC and AB = 24, what is the length of the segment from G to the midpoint of AB?

Back

8 units (one third of the median).

Front

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

Back

The segment from the vertex to the centroid is twice as long as the segment from the centroid to the midpoint of the opposite side.

Front

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

Back

9 (since AZ is twice ZX).

Front

What type of segments are drawn from the vertices to the opposite sides in a triangle?

Back

Medians.

Front

If AC = 32 and G is the centroid, what is the length of CE?

Back

16 (half of AC).

Front

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

Back

Length of median / 3.