Similarity of Medians in Triangles

Similarity of Medians in Triangles

How to solve the similarity of medians in triangles problems: definition, example, and its solution.

Definition

The median of a triangle is a line segment that starts from the vertex and ends at the midpoint of the opposite side.

The median of a triangle is a line segment
that starts from the vertex
and ends at the midpoint of the opposite side.

Example

If triangle ABC ~ triangle A'B'C', find the value of x. The measure of the side of the left triangle: 5. The measure of the median of the left triangle: 4. The measure of the side of the right triangle: 7. The measure of the median of the right triangle: x.

If two triangles are similar,
then their medians are proportional.

So the medians and the sides are proportional:
4 / x = 5 / 7.