**Definition of Similar Figures**

- Similar figures are figures that have the same shape but not necessarily the same size.

**Examples of Similar Figures**

- The trapezoids shown below are similar; they have the same shape but they are different in size.

**More about Similar Figures**

- Any two corresponding sides in two similar figures have a common ratio called the scale factor.

The trapezoids ABCD and EFGH shown above are similar. So, . - The ratio of areas of two similar figures is the square of the scale factor.
- The ratio of volumes of two similar figures is the cube of the scale factor.

**Solved Example on Similar Figures**

Find the value of

x, if the figures are similar.

Choices:

A.

B.

C.

D.

Correct Answer: B

Solution:

Step 1:Since the figures are similar, the ratios of the lengths of corresponding sides of the figures are equal.

Step 2:[Write the proportion.]

Step 3:[Substitute the values.]

Step 4:12 ×x= 5 × 6 [Write the cross products.]

Step 5:[Divide both sides by 12.]

Step 6:[Simplify.]

Step 7:[Convert improper fraction into mixed number.]

Step 8:The value ofxis .

**Related Terms for Similar Figures**

- AA Similarity Postulate
- SAS Similarity Postulate
- SSS Similarity Postulate