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## Is a rigid transformation always congruent?

We now know that the rigid transformations (reflections, translations and rotations) preserve the size and shape of the figures. That is, **the pre-image and the image are always congruent**.

## Are congruence transformation and rigid transformation the same operations?

A transformation is an operation that moves, flips, or otherwise changes a figure to create a new figure. A rigid transformation (also known as an isometry or congruence transformation) is a transformation that does not change the size or shape of a figure.

## Does any sequence of rigid transformations result in a congruence transformation?

Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (that is, by a sequence of reflections, translations, and/or **rotations**).

## Which transformations result in a congruence transformation?

There are three main types of congruence transformations: **reflections (flips), rotations (turns), and translations (slides)**. These congruence transformations can be used to obtain congruent shapes or to verify that two shapes are congruent.

## What does congruence have to do with rigid transformations?

When a figure is transformed with one or more rigid transformations, **an image is created that is congruent to the original figure**. In other words, two figures are congruent if a sequence of rigid transformations will carry the first figure to the second figure.

## Which transformation is not a congruence transformation?

The only choice that involves changing the size of a figure is letter a) **dilation** and as a result, creates two figures that are NOT congruent. The other three choices merely “move” a shape to a new location (i.e. rotated, translated, or reflected) and result in a congruent figure.

## What is rigid transformations and congruence?

In describing images of figures under rigid transformations on and off square grids and the coordinate plane, students use the terms “corresponding points,” “corresponding sides,” and “image.” Students learn that **angles and distances are preserved by any sequence of translations, rotations, and reflections**, and that …

## Why is a rigid motion also called a congruence transformation?

Congruence Transformations

Another name for a rigid motion or a combination of rigid motions is a congruence transformation **because the preimage and image are congruent**. The terms “rigid motion” and “congruence transformation” are interchangeable.