# Similar Triangles

Two triangles are similar if they have the same shape but different size.

Their corresponding angles are equal.

Two triangles are similar if:

Their corresponding sides are proportional, that is to say, they have the same ratio.

The perimeters of similar triangles have the same ratio.

The ratio of areas of similar triangles is equal to the square of the ratio.

#### Problems

1. Calculate the height of a building that casts a shadow of 6.5 meters if at the same time and in the same place a pole of 4.5 m in height produces a shadow of 0.90 m.

2.The legs of a right triangle measure 24 m and 10 m. What is the length of the legs of a similar triangle to this one whose hypotenuse is 52 m?

## Similar Triangle Rules

1Two triangles are similar if two angles are equal.

2 Two triangles are similar if the sides are proportional.

3 Two triangles are similar if two sides are proportional and the angle between them is equal.

#### Examples

Determine whether the following triangles are similar:

The triangles are similar because the sides are proportional.

180º − 100º − 60º = 20º

They are similar triangles because they have two equal angles.

They are similar because two sides are proportional and the angle between them is equal.

## Similar Right Triangles

1Two right triangles are similar if they have an equal acute angle.

2Two right triangles are similar if they have two legs that are proportional.

3Two right triangles are similar if the ratio of the hypotenuses and the legs are proportional.