Question

quadrilateral abcd is rotated 145° about point t. the result is quadrilateral abcd. which congruency statement is correct?abcd ≅ abcdabcd ≅ adcbcdab ≅ adcbcdab ≅ 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. That is, quadrilateral \(ABCD\) and quadrilateral \(A'B'C'D'\) are congruent. Also, when we name congruent polygons, the order of the vertices must correspond.

Step2: Analyze the vertex correspondence

When quadrilateral \(ABCD\) is rotated to get \(A'B'C'D'\), \(A\) corresponds to \(A'\), \(B\) corresponds to \(B'\), \(C\) corresponds to \(C'\), and \(D\) corresponds to \(D'\).

Answer:

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