Medians and Altitudes (5.4)

Front

What is the centroid of a triangle?

Back

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

Front

How many segments does the centroid divide each median into?

Back

The centroid divides each median into two segments.

Front

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

Back

The shorter segment is one third the length of the entire median.

Front

If AZ = 24 and X is the centroid, what is the length of AX?

Back

AX = 16.

Front

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

Back

AZ = 9.

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

How many medians does a triangle have?

Back

A triangle has three medians.

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.

Front

What is the formula to find the length of a median in a triangle?

Back

The length of a median can be calculated using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), 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 significance of the centroid in a triangle?

Back

The centroid is the center of mass of the triangle and is the point where the triangle balances.