Question

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

Explanation:

Step1: Recall the property of rotation

Rotation is a rigid transformation. Rigid transformations (rotations, translations, reflections) preserve the shape and size of a figure. So, the pre - image and the image are congruent. Also, the order of the vertices in the congruence statement should match the order of the corresponding vertices.

Step2: Analyze each option

• For the congruence statement \(ABCD\cong A'B'C'D'\), the order of vertices \(A\to A'\), \(B\to B'\), \(C\to C'\), \(D\to D'\) does not match the rotation correspondence.
• For the congruence statement \(ABCD\cong A'D'C'B'\), the order of vertices does not match the rotation correspondence.
• For the congruence statement \(CDAB\cong A'D'C'B'\):
• When we rotate the quadrilateral \(ABCD\) about point \(T\) by \(145^{\circ}\), vertex \(C\) corresponds to \(A'\), vertex \(D\) corresponds to \(D'\), vertex \(A\) corresponds to \(C'\) and vertex \(B\) corresponds to \(B'\).
• For the congruence statement \(CDAB\cong C'B'AD'\), the order of vertices does not match the rotation correspondence.

Answer:

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