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 3, what does that mean?

Back

It means that each side of the larger figure is 3 times the length of the corresponding side of the smaller figure.

Front

How do you find the missing side length in similar figures?

Back

To find the missing side length, set up a proportion using the scale factor and the known side lengths.

Front

If the scale factor from figure A to figure B is 4, and the length of a side in figure A is 5, what is the length of the corresponding side in figure B?

Back

The length of the corresponding side in figure B is 5 x 4 = 20.

Front

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

Back

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

Front

If the scale factor is 2, what is the ratio of the areas of the two similar figures?

Back

The ratio of the areas is 2^2 = 4.

Front

Find x if the sides of two similar triangles are in the ratio 3:5 and one side of the smaller triangle is 9. What is x?

Back

x = 9 x (5/3) = 15.

Front

If triangle ABC is similar to triangle DEF and the lengths of sides are in the ratio 1:2, what is the scale factor?

Back

The scale factor is 2.

Front

If the length of a side in a smaller figure is 6 and the corresponding side in a larger figure is 18, what is the scale factor?

Back

The scale factor is 18/6 = 3.