Similar Figures and Proportional Relationships

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 sides are equal.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if they have the same shape, which can be determined by checking if their corresponding angles are equal (AA criterion) or if the sides are in proportion (SSS or SAS criteria).

Front

What is the AA criterion for triangle similarity?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the SSS criterion for triangle similarity?

Back

The SSS criterion states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

What is the SAS criterion for triangle similarity?

Back

The SAS criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

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

Back

A scale factor of 2 means that each side of the larger figure is twice the length of the corresponding side of the smaller figure.

Front

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

Back

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

Front

If triangle ABC is similar to triangle DEF, and AB = 4 cm, DE = 8 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

What is a proportion?

Back

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