Similar Figures and Scale Factor

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In the context of similar figures, it is the ratio of the lengths of corresponding sides.

Front

If two similar figures have a scale factor of 2, what does that mean?

Back

It means that each side of the larger figure is twice as long as the corresponding side of the smaller figure.

Front

How do you find the scale factor between two similar figures?

Back

To find the scale factor, divide the length of a side of the larger figure by the length of the corresponding side of the smaller figure.

Front

If the scale factor is 5, and the length of a side in the smaller figure is 4, what is the length of the corresponding side in the larger figure?

Back

The length of the corresponding side in the larger figure is 20 (5 x 4 = 20).

Front

If a triangle has sides of lengths 3, 4, and 5, and is similar to another triangle with a side of length 12, what is the length of the corresponding side?

Back

The corresponding side is 16 (12 is 4 times the scale factor of 3).

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of their areas is equal to the square of the scale factor.

Front

If the scale factor is 10, what is the ratio of the areas of the two similar figures?

Back

The ratio of the areas is 100 (10^2 = 100).

Front

If a rectangle has a length of 8 and a width of 4, and is similar to another rectangle with a length of 40, what is the width of the larger rectangle?

Back

The width of the larger rectangle is 20 (40 is 5 times the scale factor of 8).

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.