# Homework 2 Similar Figures Math

The two figures that have same shape but different size are said to be similar. The angles of similar figures measure the same but corresponding sides are in proportion i.e when two figures are similar the ratio of the length of the corresponding sides are equal. Any two corresponding sides of two similar figures have a common ratio called the scale factor. The symbol ~ is used to represent corresponding similar sides.

The trapezoids ABCD and GHIJ are similar. So,

This means the length of sides of the trapezoid ABCD is 2 times the length of the sides of the trapezoid GHIJ.

The ratio of area of two similar figures is the square of the scale factor and the ratio of the volume of two similar figures is cube of the scale factor.

Solution:

Note:

Corresponding angles are marked in the same way in diagrams.

Example 11

Find the value of the pronumeral in the following diagram.

##### Solution:

Problem Solving

#### Example 12

Find the value of the height, *h* m, in the following diagram at which the tennis ball must be hit so that it will just pass over the net and land 6 metres away from the base of the net.

##### Solution:

So, the height at which the ball should be hit is 2.7 m.

Example 13

Adam looks in a mirror and sees the top of a building. His eyes are 1.25 m above ground level, as shown in the following diagram.

If Adam is 1.5 m from the mirror and 181.5 m from the base of the building, how high is the building?

##### Solution:

So, the height of the building is 150 m.

Note:

a. Equal angles are marked in the same way in diagrams.

b. Two triangles are similar if:

- two pairs of corresponding sides are in the same ratio and the angle included between the sides is the same for both triangles.
- the corresponding sides are in the same ratio.
- the corresponding angles are the same.

Key Terms

similar figures, scale factor, equiangular, similar triangles

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