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

How do you determine if two triangles are similar?

Back

Two triangles are similar if they satisfy one of the following criteria: AA (Angle-Angle) criterion, SSS (Side-Side-Side) similarity criterion, or SAS (Side-Angle-Side) similarity criterion.

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 corresponding sides of two triangles are in proportion, 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

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

Back

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

Front

If two triangles are similar and one side of the first triangle is 6 cm and the corresponding side of the second triangle is 9 cm, what is the scale factor?

Back

The scale factor is 9/6 or 3/2.

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 triangles are in the ratio 2:3, what is the ratio of their areas?

Back

The ratio of their areas is 2^2:3^2, which simplifies to 4:9.

Front

How can you use proportions to solve for a missing side in similar triangles?

Back

Set up a proportion using the known side lengths of the similar triangles, cross-multiply, and solve for the missing side.