Dilations & Similar Triangles

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces a figure similar to the original by enlarging or reducing it, using a center point and a scale factor.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the scale factor in a dilation?

Back

The scale factor is the ratio of the lengths of corresponding sides of the original figure to the dilated figure.

Front

If a triangle has sides of lengths 3, 4, and 5, what are the lengths of the sides of a triangle similar to it with a scale factor of 2?

Back

The lengths of the sides would be 6, 8, and 10.

Front

True or False: A dilation produces a congruent figure.

Back

False. A dilation produces a similar figure, not necessarily congruent.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 and side DE is 8, what is the scale factor?

Back

The scale factor is 2.

Front

How do you determine if two triangles are similar using the Side-Angle-Side (SAS) similarity criterion?

Back

Two triangles are similar if one angle is equal and the sides including that angle are in proportion.

Front

What is the algebraic representation of a dilation with a scale factor of 0.5?

Back

(x, y) -> (0.5x, 0.5y)