SIMILAR FIGURES

Similar Figures

Definition Of Similar Figures

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

Video Examples: Similar Figures and Proportions

Example of Similar Figures

Find the value of x, if the figures are similar.

Solved Example on Similar Figures

Ques: Find the number of Similar Figures in the measurement 4.07 cm.

Choices:

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 .

Quick Summary

Similar figures have the same shape but different sizes.
Corresponding sides of similar figures are proportional.
The ratio of corresponding sides is called the scale factor.
Ratio of areas of similar figures is the square of the scale factor.
Ratio of volumes of similar figures is the cube of the scale factor.

\[ \frac{a}{b} = \frac{c}{d} \]

🍎 Teacher Insights

Use hands-on activities like scaling images or creating similar triangles to help students visualize the concept. Emphasize the importance of correctly identifying corresponding sides and angles.

🎓 Prerequisites

Ratios
Proportions
Basic Geometric Shapes

Check Your Knowledge

Q1: Two triangles are similar. The sides of the smaller triangle are 3, 4, and 5. The longest side of the larger triangle is 10. What is the perimeter of the larger triangle?

12 18 24 36

Q2: If two squares are similar, and the side length of the first is 2 and the second is 6, what is the ratio of their areas?

1:3 1:6 1:9 1:12

Frequently Asked Questions

Q: What does it mean for figures to be similar?
A: Similar figures have the same shape, but can be different sizes. All corresponding angles are equal, and corresponding sides are in proportion.

Q: How do you find the scale factor between two similar figures?
A: Divide the length of a side in one figure by the length of the corresponding side in the other figure. Make sure you are comparing corresponding sides.