Dilation and Similarity

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but not its shape, using a scale factor.

Front

What does similarity mean in geometry?

Back

Similarity means that two figures have the same shape but may differ in size.

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, the triangles are similar.

Front

What is the SSS criterion for triangle similarity?

Back

The SSS criterion states that if the sides of one triangle are proportional to the sides of another triangle, 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 proportional to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, a quantity. In dilation, it determines how much larger or smaller a figure becomes.

Front

If a triangle has sides of lengths 3, 4, and 5, and another triangle has sides of lengths 6, 8, and 10, are they similar?

Back

Yes, they are similar by the SSS criterion because the sides are in proportion (3:6, 4:8, 5:10).

Front

What is the similarity statement for triangles ΔABC and ΔDEF if they are similar?

Back

ΔABC~ΔDEF.

Front

How do you determine if two figures are similar?

Back

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

Front

What happens to the area of a figure when it is dilated by a scale factor of k?

Back

The area of the figure is multiplied by k².