Question

quadrilateral abcd is rotated 145 about point t. the result is quadrilateral abcd. which congruency statement is correct? cdab ≅ cbad abcd ≅ adcb cdab ≅ adcb abcd ≅ abcd

Explanation:

Step1: Understand the property of rotation

Rotation is a rigid transformation. Rigid transformations (such as rotation) preserve the shape and size of a figure. So, the pre - image (quadrilateral \(ABCD\)) and the image (quadrilateral \(A'B'C'D'\)) after rotation are congruent.

Step2: Check the congruency statement format

The order of the vertices in the congruency statement should match. Since \(ABCD\) is rotated to get \(A'B'C'D'\), the congruency statement should be \(ABCD\cong A'B'C'D'\).

Let's analyze the other options:

• For \(CDAB\cong C'B'A'D'\), the order of vertices is not in the correct correspondence.
• For \(ABCD\cong A'D'C'B'\), the order of vertices is not in the correct correspondence.
• For \(CDAB\cong A'D'C'B'\), the order of vertices is not in the correct correspondence.

Answer:

\(ABCD\cong A'B'C'D'\)