Similarity and Dilations

Front

What is the definition of similarity in geometry?

Back

Similarity in geometry refers to figures that have the same shape but may differ in size. Corresponding angles are equal, and corresponding sides are proportional.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In the context of similar figures, it is the ratio of the lengths of corresponding sides.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

What does the AA criterion for similarity state?

Back

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

Front

What does the SAS criterion for similarity state?

Back

The SAS (Side-Angle-Side) criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What does the SSS criterion for similarity state?

Back

The SSS (Side-Side-Side) criterion states that if the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

How do you find the scale factor between two similar figures?

Back

To find the scale factor, divide the length of a side of one figure by the length of the corresponding side of the other figure.

Front

If the scale factor from triangle ABC to triangle DEF is 3/2, what does this mean?

Back

This means that each side of triangle DEF is 1.5 times longer than the corresponding side of triangle ABC.

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 scale factor.

Front

If triangle XYZ is similar to triangle PQR with a scale factor of 1/4, what is the ratio of their areas?

Back

The ratio of their areas is (1/4)² = 1/16.