Dilations and Similarity

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center point and a scale factor.

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is the AA similarity criterion?

Back

The AA (Angle-Angle) similarity 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 Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, segment AB is congruent to segment AB.

Front

How do you determine if triangles are similar using side lengths?

Back

To determine if triangles are similar using side lengths, check if the ratios of the lengths of corresponding sides are equal.

Front

What is the relationship between corresponding angles in similar triangles?

Back

In similar triangles, corresponding angles are equal.

Front

What is the SAS similarity criterion?

Back

The SAS (Side-Angle-Side) similarity 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 it mean for two figures to be congruent?

Back

Two figures are congruent if they have the same shape and size, meaning all corresponding sides and angles are equal.

Front

What is the relationship between dilations and congruence?

Back

Dilations do not produce congruent figures; they produce similar figures that may be larger or smaller but maintain the same shape.