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: Analyze Transformations

Trapezoid CDEF is reflected over x - axis and rotated 90° about origin. Reflections and rotations are rigid transformations, so corresponding vertices must match.

Step2: Identify Corresponding Vertices

• After reflection over x - axis, the y - coordinates change sign. Then, a 90° rotation (counter - clockwise, assuming standard) about origin transforms (x,y) to (-y,x).
• Let's track the vertices:
• Vertex C of CDEF should correspond to vertex N of the other trapezoid.
• Vertex D of CDEF should correspond to vertex M of the other trapezoid.
• Vertex E of CDEF should correspond to vertex O of the other trapezoid.
• Vertex F of CDEF should correspond to vertex P of the other trapezoid.
• So, the congruence statement should map C→N, D→M, E→O, F→P. So CDEF ≅ NMOP.

Answer:

CDEF ≅ NMOP