Similar Figures and Proportions

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 the lengths of their corresponding sides are proportional.

Front

What does it mean for two figures to be proportional?

Back

Two figures are proportional if the ratios of their corresponding side lengths are equal.

Front

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

Back

To find a missing side length, set up a proportion using the lengths of corresponding sides from the similar figures and solve for the unknown.

Front

If two triangles are similar, what can you say about their angles?

Back

If two triangles are similar, their corresponding angles are equal.

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 figures is 3:2, what does this mean?

Back

This means that for every 3 units of length in the larger figure, there are 2 units of length in the smaller figure.

Front

How do you solve for a variable in a proportion?

Back

Cross-multiply the terms in the proportion and then isolate the variable to solve for it.

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 the sides of two similar rectangles are in the ratio 4:5, what is the ratio of their areas?

Back

The ratio of their areas is 16:25, since (4^2):(5^2) = 16:25.

Front

What is a proportion?

Back

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