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 Rotation Congruence

A rotation is a rigid transformation, so the image (A'B'C'D') is congruent to the pre - image (ABCD), and the corresponding vertices must be in order. When a figure is rotated, each vertex of the pre - image maps to a corresponding vertex of the image. So vertex A maps to A', B maps to B', C maps to C', and D maps to D'.

Step2: Analyze Congruence Statements

• For the statement \(ABCD\cong A'B'C'D'\), the order of the vertices is preserved (A to A', B to B', C to C', D to D'), which is correct for a rotation (a rigid transformation that preserves the shape and size, and the order of corresponding vertices).
• For \(ABCD\cong A'D'C'B'\), the order of vertices is not preserved (A maps to A', not D'; B maps to B', not C' etc.), so this is incorrect.
• For \(CDAB\cong A'D'C'B'\), the order of vertices in the pre - image (CDAB) and the image (A'D'C'B') does not match the correspondence from rotation.
• For \(CDAB\cong C'B'A'D'\), the order of vertices does not match the correspondence from rotation.

Answer:

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