Question

writing a congruency statement trapezoid cdef was reflected across the x - axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. which congruency statement applies to the trapezoids? cdef ≅ npom cdef ≅ mnpo cdef ≅ nmop cdef ≅ mopn

Explanation:

Step1: Understand congruence transformations

Reflections and rotations are rigid transformations. Rigid transformations preserve the shape and size of a figure, so the pre - image (trapezoid CDEF) and the image (the other trapezoid) are congruent. We need to match the vertices correctly.

Step2: Match the vertices

When we perform a reflection across the \(x -\)axis and then a \(90^{\circ}\) rotation about the origin, we can observe the vertex - to - vertex correspondence.
Let's assume the order of vertices in the congruence statement should follow the order of corresponding vertices.
For trapezoid CDEF, after the transformation, the vertices correspond as \(C\to N\), \(D\to M\), \(E\to O\), \(F\to P\)

Answer:

CDEF ≅ NMOP