Median, Centroid, Midsegments

Front

What is the centroid of a triangle?

Back

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

Front

What is a median in a triangle?

Back

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

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 longer segment being twice the length of the shorter segment (2:1 ratio).

Front

If G is the centroid of triangle ABC, what is the ratio of AG to GD?

Back

The ratio of AG to GD is 3:1.

Front

If AD = 30 in triangle ABC, what is the length of AG?

Back

AG = 20.

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle.

Front

How does the length of a midsegment compare to the lengths of the sides of the triangle?

Back

The length of a midsegment is half the length of the side it is parallel to.

Front

If AB = 16, what is the length of QS if QS is a midsegment?

Back

QS = 32.

Front

If TP = 27, what is the length of ZP if ZP is a midsegment?

Back

ZP = 9.

Front

What is the formula for finding 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.