Geometry Chapter 5 5-3 Medians and Centroids

Front

What is a median in a triangle?

Back

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

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the center of mass of the triangle.

Front

If BM = 21, what is PM?

Back

7

Front

The centroid is the point of concurrency of the 3 ____ of a triangle.

Back

Medians

Front

If CF, BE, and AD are the medians of the triangle and CE = 15, find AE.

Back

15

Front

If G is the centroid of triangle ABC and AC= 32, find the length of CE.

Back

16

Front

If AC = 16, what is AM?

Back

8

Front

How do you find the length of a median in a triangle?

Back

To find the length of a median, use the formula: m = 1/2 * √(2a² + 2b² - c²), where a and b are the lengths of the sides adjacent to the median, and c is the length of the opposite side.

Front

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

Back

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

Front

What is the formula for finding the centroid of a triangle given its vertices?

Back

The centroid (G) can be found using the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3), where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.