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a. Are ABCDE and JKLMN congruent? If so, describe a composition of rigid motions that maps ABCDE to JKLMN....

a. Are ABCDE and JKLMN congruent? If so, describe a composition of rigid motions that maps ABCDE to JKLMN. If not, explain.
b. Are ABCDE and VWXYZ congruent? If so, describe a composition of rigid motions that maps ABCDE to VWXYZ. If not, explain.

Answer

  1. ABCDE and JKLMN: Yes, ABCDE and JKLMN are congruent. A possible composition of rigid motions is a translation followed by a rotation. First, translate ABCDE so that point A coincides with point J. Then, rotate the figure around point J until the orientation matches JKLMN.

  2. ABCDE and VWXYZ: No, ABCDE and VWXYZ are not congruent. The shapes have different side lengths and angles, which means they cannot be mapped onto each other using rigid motions.

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