Similar Figures

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 proportional.

Front

What does it mean for sides to be proportional?

Back

Sides are proportional when the ratios of the lengths of corresponding sides of two figures are equal.

Front

If two triangles have sides of lengths 3 cm, 4 cm, and 5 cm, and 6 cm, 8 cm, and 10 cm, are they similar?

Back

Yes, they are similar because the ratios of the corresponding sides (3:6, 4:8, 5:10) are all equal to 1:2.

Front

How do you find the missing side of a similar figure?

Back

To find the missing side, set up a proportion using the lengths of the corresponding sides of the similar figures.

Front

What is the formula for finding the scale factor between two similar figures?

Back

The scale factor is found by dividing the length of a side of one figure by the length of the corresponding side of the other figure.

Front

If the scale factor of two similar rectangles is 3:5, what does this mean?

Back

This means that for every 3 units of length in the smaller rectangle, there are 5 units of length in the larger rectangle.

Front

Can two figures be similar if they have different shapes?

Back

No, two figures cannot be similar if they have different shapes. They must have the same shape.

Front

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

Back

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

Front

If two similar figures have a side length ratio of 1:4, what is the ratio of their areas?

Back

The ratio of their areas is 1:16, since (1^2):(4^2) = 1:16.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.