#4.6 Similarity and 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 maintains its shape. Examples include translations, rotations, reflections, and dilations.

Front

What is the definition of 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 does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. This means 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 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 a reflection in geometry?

Back

A reflection is a transformation that flips a figure over a line, creating a mirror image. The line is called the line of reflection.

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle in a specified direction.

Front

What is the difference between a translation and a reflection?

Back

A translation moves a figure from one location to another without changing its shape, size, or orientation, while a reflection flips the figure over a line, creating a mirror image.

Front

What is the effect of a 180° rotation on a figure?

Back

A 180° rotation turns a figure around a point so that each point moves to a position directly opposite its original position, effectively flipping the figure.

Front

What is the result of a reflection followed by a dilation?

Back

The result is a figure that is first flipped over a line (reflection) and then resized (dilation) according to the scale factor.

Front

What is NOT a similarity transformation?

Back

A translation and a reflection together are not considered a similarity transformation because they do not maintain the same orientation.