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How to Identify Isometries

Instructor: Melanie Olczak

Melanie has taught high school Mathematics courses for the past ten years and has a master's degree in Mathematics Education.

This lesson defines an isometry as a transformation that does not change the size or shape of an image. In this lesson we look at the three transformations that are isometries and the one that is not, in order to explain how to identify an isometry. Examples and non-examples of isometries are also provided.

Did you know that if you take any two dimensional shape, you can move, flip or turn that figure and still end up with the same shape? An isometry is a transformation that does not change the size or shape of an image. There are three transformations that are isometries.

The first transformation that is an isometry is called a translation. A translation is moving all the points of the image the same distance in the same direction, or in other words, a slide.

Translation
congruent

Translations can also be done in the coordinate plane. We can take the triangle ABC with coordinates A(1,1), B(3, 1) and C(1,5) and we can translate it six units to the left and four units down. Both triangles are still the same, however their locations are different.

Trans Coordinate Plane

The second transformation that is an isometry is called a reflection. A reflection is flipping an object or figure over a line or a point. Just like if you were to look at your reflection in a mirror, the image you see is an exact copy of yourself, as long as you aren't looking at a funhouse or carnival mirror.

Reflection

Reflections can also be done in the coordinate place. We can take the same triangle we used above with coordinates A(1,1), B(3, 1) and C(1,5) and we can reflect it over the x-axis. All of the points will now be the same distance from the x-axis, but on the other side of it.

Reflection

The third transformation that is an isometry is called a rotation. A rotation is a turn. Objects and figures can be rotated any number or degrees around a certain point. If we take the same object and turn it, the size and shape of the object does not change. We can also rotate an image in the coordinate plane.

Rotation
Rotation Coordinate Plane

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