Honors Geometry - Similarity Transformations

Front

What is a similarity transformation?

Back

A similarity transformation is a geometric transformation that alters the size and/or position of a figure but preserves its shape. Examples include translations, rotations, reflections, and dilations.

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 symbol used to denote similarity between two figures?

Back

The symbol for similarity is '∼'. For example, if triangle ABC is similar to triangle DEF, it is written as ΔABC ∼ ΔDEF.

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 is the effect of a reflection on a geometric figure?

Back

A reflection flips a figure over a line (the line of reflection), creating a mirror image of the original figure.

Front

What is the difference between congruence and similarity?

Back

Congruent figures are identical in shape and size, while similar figures have the same shape but may differ in size.

Front

What transformations keep figures congruent?

Back

Transformations that keep figures congruent include translations, rotations, and reflections.

Front

What is the relationship between the angles of similar triangles?

Back

In similar triangles, corresponding angles are equal.

Front

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

Back

Two triangles are similar if the ratios of the lengths of their corresponding sides are equal.