When two shapes are similar, they have the same shape but may be different sizes. This means that all corresponding dimensions are in the same ratio. This applies to both 2-D shapes and 3-D shapes and it is used to find missing lengths.

 

 

What Corresponding Dimensions Means

Corresponding dimensions are lengths that match in position and role within each shape.

 

For example, a base matches a base and a height matches a height. In 3-D shapes, matching edges correspond.

 

Always compare like with like.

 

Identify the matching sides before you use any ratios

 

 

Ratios in Similar 2-D Shapes

In similar 2-D shapes, all corresponding side lengths are in the same ratio and all corresponding angles are equal.

 

If one pair of corresponding sides has a known ratio, then every other pair of corresponding sides must use the same ratio.

 

Example scale factor written as:

$$
\frac{3}{2}
$$

 

 

Using Ratios to Find Missing Lengths

To find a missing length, form a ratio using a pair of known corresponding sides, then apply the same ratio to the unknown length.

 

Example scale factor from 4 cm to 10 cm:

$$
\frac{10}{4}
$$

 

The same scale factor must be applied to every corresponding length.

 

 

Ratios in Similar 3-D Shapes

In similar 3-D shapes, corresponding edge lengths are also in the same ratio.

 

If one edge length changes by a scale factor, then every other corresponding edge length changes by the same scale factor.

 

Only lengths scale directly in this way

 

 

Important Distinction

This topic is about dimensions, meaning lengths only.

 

Areas and volumes do not scale by the same factor as lengths, so do not use a length ratio to compare areas or volumes.

 

 

Common Errors to Avoid

Common mistakes include comparing sides that do not correspond, using different ratios for different sides and assuming shapes are similar without checking angles.

 

 

Key Points to Remember

Similar shapes have corresponding dimensions in the same ratio.
Only corresponding lengths should be compared.
The same ratio applies to every matching dimension.
This applies to both 2-D and 3-D shapes.
Correct use of ratios allows missing lengths to be found accurately.

 

Using corresponding dimension ratios correctly makes enlargement and similar shape problems much more straightforward.