Transformations, Similarity, and Congruence

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape to create a new shape. Common transformations include translations, rotations, reflections, and dilations.

Front

Define congruent figures.

Back

Congruent figures are shapes that are identical in shape and size. They can be transformed into one another through rotations, translations, or reflections.

Front

What is similarity in geometry?

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 a dilation?

Back

A dilation is a transformation that changes the size of a figure but keeps its shape. It involves a scale factor that determines how much the figure is enlarged or reduced.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if their corresponding sides and angles are equal. This can be proven using various congruence criteria such as SSS, SAS, ASA, AAS, or HL.

Front

What is the difference between congruence and similarity?

Back

Congruence means that figures are the same size and shape, while similarity means that figures have the same shape but may differ in size.

Front

What is a reflection in geometry?

Back

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

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.

Front

What is a translation in geometry?

Back

A translation is a transformation that slides a figure from one position to another without changing its shape, size, or orientation.

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 less than 1 reduces it.