Identify Similar Shapes

Shapes that have the same size angles but are enlargements of each other are are called similar.

 

 

The squares below are similar because each have four angles of 90^o and are enlargements of each other.

 

 

So, what does not similar look like?

One triangle below is not similar to the others because it is not an enlargement of the others.

 

 

Easy to spot, wasn't it?

 

When we enlarge a shape we use a multiplier. 

We call it a scale factor.

 

For example, let's say we have two similar triangles and they have the heights shown below:

 

 

We can see that they look similar.

The scale factor is 4 ÷ 2 = 2

That means that the height of the big triangle is 2 times greater than the height of the small one.

 If the base of the big triangle is also 2 times bigger, then it confirms that they are indeed similar triangles.

 

Let's look at a question!

 

Example

Are the shapes below similar?

What is the scale factor?

 

 

Answer

They certainly look similar!

We can check by finding the scale factor.

 

Large height ÷ Small height = 6 ÷ 2 = 3

Large base ÷ Small base = 3 ÷ 1 = 3

 

Both answers have a scale factor of 3, so they are similar!

Scale factor 3 means that all the sides of the rectangles are 3 times longer on the large one!

 

Let's try some questions like this!