Question

determining if figures are congruent are rectangles abcd and wxyz congruent? why or why not? yes, all right angles were preserved. yes, both rectangles have an area of 24 square units. yes, a 180° rotation about the origin will map abcd to wxyz. no, there is not a rigid transformation or a combination of rigid transformations that will map abcd to wxyz.

Explanation:

Step1: Recall congruence definition

Two figures are congruent if there is a rigid - transformation (translation, rotation, reflection) or a combination of them that maps one figure onto the other. Rigid transformations preserve side - lengths and angles.

Step2: Analyze side - lengths

Rectangle ABCD has side - lengths that are different from rectangle WXYZ. Just because angles are right angles (preserved in both rectangles) or areas are equal does not mean the rectangles are congruent. A 180 - degree rotation about the origin will not map ABCD to WXYZ since their side - lengths and orientations (even if we consider rotation) do not match.

Answer:

No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.