Geometry | Unit 1 | Lesson 11: Defining Reflections | Practice Problems

Front

What is a rigid transformation in geometry?

Back

A rigid transformation is a transformation that preserves the shape and size of a figure, meaning the original figure and the transformed figure are congruent. Examples include translations, rotations, and reflections.

Front

What is a reflection in geometry?

Back

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

Front

How do you identify a line of reflection between two points A and B?

Back

The line of reflection can be identified by constructing the perpendicular bisector of the segment connecting points A and B.

Front

What is the difference between rigid and non-rigid transformations?

Back

Rigid transformations preserve the size and shape of figures (e.g., translations, rotations, reflections), while non-rigid transformations can change the size or shape (e.g., dilations, stretching).

Front

What is the perpendicular bisector of a segment?

Back

The perpendicular bisector of a segment is a line that divides the segment into two equal parts at a right angle.

Front

Can a reflection change the size of a figure?

Back

No, a reflection does not change the size of a figure; it only changes its orientation.

Front

What is the effect of a reflection on the coordinates of a point?

Back

When reflecting a point across a line, the coordinates of the point change based on the line of reflection. For example, reflecting a point across the y-axis changes the sign of the x-coordinate.

Front

What are the properties of reflections in geometry?

Back

Reflections have several properties: they preserve distances, angles, and the overall shape of figures; they create mirror images; and the line of reflection is the perpendicular bisector of the segment connecting corresponding points.

Front

How can you determine if a transformation is rigid?

Back

To determine if a transformation is rigid, check if the original figure and the transformed figure are congruent, meaning they have the same size and shape.

Front

What is an example of a non-rigid transformation?

Back

An example of a non-rigid transformation is dilation, where a figure is resized either larger or smaller.