similar figures


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 of x is .

Related Terms for Similar Figures

  • AA Similarity Postulate
  • SAS Similarity Postulate
  • SSS Similarity Postulate