Isometry Explained
Guide w/ 9 Step-by-Step Examples!

What is an isometry?

That’s the key question we’re going to solve in today’s geometry lesson.

You’re going to learn what an isometry is and is not.

Also, you’ll gain a broad overview of all types of rigid motions in a plane.

Let’s get to it!

So by definition, an isometry is a rigid transformation.

It’s true!

Going further, a transformation maps or moves an initial image (preimage) onto a final image (image).

Some of the basic mapping or moving of a figure in a plane are sliding, flipping, turning, enlarging, or reducing to create new figures.

The four major types of transformations are:

1. Translation (figure slides in any direction)
2. Reflection (figure flips over a line)
3. Rotation (figure turns about a fixed point)
4. Dilation (figure is enlarged or reduced)

But of the four basic types of transformations, only three are isometric.

• Translation
• Reflection
• Rotation

An isometry is a rigid transformation that preserves length and angle measures, as well as perimeter and area.

In other words, the preimage and the image are congruent, as Math Bits Notebook accurately states. Therefore, translations, reflections, and rotations are isometric, but dilations are not because the image and preimage are similar figures, not congruent figures.

In the video below, you’ll learn how to:

1. Name and describe the three isometric transformations.
2. Prove that a transformation is an isometry by comparing side lengths.
3. Graph an image using a given transformation.

Video – Lesson & Examples

46 min

Introduction isometry and rigid motion in a plane

00:00:35 – What is an isometry? Explained with a transformation (Example #1)

Exclusive Content for Member’s Only

• 00:15:46 – Name and describe the transformation (Examples #2-3)
• 00:23:46 – Show that the transformation is an isometry by comparing side lengths (Example #4)
• 00:31:37 – Find the value of each variable given an isometric transformation (Examples #5-6)
• 00:35:46 – Graph the image using the given the transformation (Examples #7-9)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions