In this activity, we are going to be looking at **similar **shapes and **scale factor**.

A **similar shape** has the same size angles, but the sides are proportionally bigger or smaller.

For example, the squares below are all **similar** because they have the same angles of 90^{o}, but the sides are all different lengths.

To see how many times bigger or smaller the shapes are we use **scale factor.**

__Example__

The rectangles are mathematically similar.

We can compare the sides by counting the squares

If we look at the base lengths, we can see that the bigger one is 4 and the smaller one is 2.

These are called **corresponding sides** because they are the equivalent side on the new shape.

To find out how many times bigger the big shape is we can divide the bigger base by the smaller:

4 ÷ 2 = 2

This means that the bigger rectangle has sides which are twice as long as the small one.

We call this the **scale factor (**or sf. for short)

**So, the scale factor is 2**

In this case, we have another pair of corresponding sides (the height).

So, we can check the scale factor, as it should be the same.

If **not,** then the shapes are** not **similar!

Heights are 6 and 3

6 ÷ 3 = 2

The shape is **similar **and the** scale factor is 2.**

Let's get started!