Medians of Triangles

Front

What is a median of a triangle?

Back

A median of a triangle is a segment with endpoints at a vertex and 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.

Front

If G is the centroid of triangle ABC and GF= 4, what is the length of GC?

Back

8

Front

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

Back

12

Front

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

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

Identify the special segment that connects a vertex to the midpoint of the opposite side.

Back

Median

Front

What are the three medians of a triangle?

Back

The three medians are the segments connecting each vertex to the midpoint of the opposite side.

Front

What is the point of concurrency of the three medians of a triangle called?

Back

Centroid

Front

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

Back

Use the formula: Median = 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 difference between a median and an altitude in a triangle?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude connects a vertex to the opposite side at a right angle.