# Similarity of Sides in Triangles

How to solve the similarity of sides in triangles problems: examples, and their solutions.

## Example 1

These two triangles have two congruent angles.

So, by the AA similarity,

these two triangles are similar.

Then their corresponding sides are proportional:

4 / 6 = 5 / *x*.

## Example 2

The red angles are vertical angles.

So they are congruent.

The red dot angles are

alternate interior angles in parallel lines.

So they are also congruent.

Then, by the AA similarity,

the purple triangle and the blue triangle are similar.

So their corresponding sides are proportional:

7 / 14 = (3*x* + 2) / 16.

## Example 3

From the given figure,

find two triangle that are congruent:

the little triangle and the whole triangle.

The red acute angles are the same angle.

And both triangle have the right angle.

So, by the AA similarity,

these two triangles are similar.

Then their corresponding sides are proportional:

3 / 7 = 5 / (5 + *x*).