Medians of Similar Triangles

Medians of Similar Triangles

How to find the medians of similar triangles: 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 connects
a vertex and the midpoint of the opposite side.

Example

If the given triangles are similar, find the value of x. [medians of triangles] = 4, x. [sides of triangles] = 5, 7.

It says these two triangles are similar.
So write [ ~ ] between the triangles.

Then their medians and sides are proportional.

The medians are 4 and x.
The sides are 5 and 7.

So 4/x = 5/7.

Solve the proportion.

Then 5x is equal to, 4⋅7, 28.

Proportion

Divide both sides by 5.

Then x = 28/5.