A rigid transformation can also be referred to as an isometric transformation. The prefix "iso-" means "of the same" and "-metric" means "measure." How does the meaning of the word isometric relate to determining if an isometric transformation occurred?

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An isometric transformation creates an image that is congruent to the pre-image. All corresponding line segments and angle measures are equal. 

The meaning of the word isometric relate to determining if an isometric transformation occurred if and only if the measures of the final figure are the same of the original figure the transformation was rigid.

What is isometric transformation?

An isometric transformation or isometry is a shape preserving transformation (movement) in the pane or space. the isometric transformation are reflection, rotation and translation and combinations of them such as the glide, which is the combination of a translation and a reflection.

Now it is said that "iso-" means "of the same" and "-metric" means "measure.

So,  when a rigid transformation occurs all the measures of the original figure (which will be transformed) will be the same of the new figure (the result of the transformation).

That means you can verify that the transformation used was rigid by checking the measures of both (original and transformed) figures: if and only if the measures of the final figure are the same of the original figure the transformation was rigid.

So,The meaning of the word isometric relate to determining if an isometric transformation occurred if and only if the measures of the final figure are the same of the original figure the transformation was rigid.

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