Similarity

Front

What is similarity in geometry?

Back

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

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if their corresponding angles are congruent and the lengths of their 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 the scale factor from triangle ABC to triangle DEF is 2, what does this mean?

Back

It means that each side of triangle DEF is twice as long as the corresponding side of triangle ABC.

Front

What is the relationship between the angles of similar figures?

Back

The angles of similar figures are congruent, meaning they have the same measure.

Front

If two rectangles are similar and the length of one is 10 cm and the length of the other is 15 cm, what is the scale factor?

Back

The scale factor is 15/10 or 3/2.

Front

How do you determine if two triangles are similar?

Back

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

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

If two similar figures have a scale factor of 1/3, what happens to their areas?

Back

The area of the smaller figure will be (1/3)² = 1/9 of the area of the larger figure.

Front

What does it mean for corresponding sides to be proportional?

Back

Corresponding sides are proportional when the ratios of their lengths are equal.