Question

triangle xyz is transformed to create triangle xyz. the side lengths of both triangles are shown.
\\( overline{xy}=10\text{ cm} ) ( overline{xy}=10\text{ cm} )
\\( overline{yz}=9\text{ cm} ) ( overline{yz}=9\text{ cm} )
\\( overline{zx}=4\text{ cm} ) ( overline{zx}=4\text{ cm} )
is this a rigid transformation? explain.
yes, the pre - image and image have the same side length measures.
yes, all transformations are rigid.
no, the side lengths of triangle xyz are different from each other.
no, each side length of xyz should be one half of the corresponding side length of xyz.

Explanation:

A rigid transformation preserves side - lengths and angles. Since $\overline{XY}=\overline{X'Y'}=10$ cm, $\overline{YZ}=\overline{Y'Z'}=9$ cm, and $\overline{ZX}=\overline{Z'X'}=4$ cm, the pre - image and image have the same side - length measures.

Answer:

Yes, the pre - image and image have the same side length measures.