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 in proportion.

Front

What does it mean for two figures to be similar?

Back

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

Front

How do you find 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 two triangles are similar, what can we say about their corresponding sides?

Back

The ratios of the lengths of their corresponding sides are equal.

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 scale factor of two similar figures is 2:3, what is the ratio of their areas?

Back

The ratio of their areas is 4:9, since (2^2):(3^2) = 4:9.

Front

How do you solve for a missing side length in similar figures?

Back

Set up a proportion using the lengths of the corresponding sides and solve for the unknown length.

Front

What is a proportion in the context of similar figures?

Back

A proportion is an equation that states that two ratios are equal, often used to compare the lengths of corresponding sides of similar figures.

Front

If triangle ABC is similar to triangle DEF, and AB = 4 cm, DE = 6 cm, what is the scale factor?

Back

The scale factor is 4:6 or 2:3.

Front

If the length of one side of a smaller similar figure is 5 cm and the corresponding side of the larger figure is 15 cm, what is the scale factor?

Back

The scale factor is 1:3.