Question

which explanation for the congruency of the trapezoids is correct? statement #1: the trapezoids are congruent because abcd was reflected over the y = x. statement #2: the trapezoids are congruent because abcd was translated left 4 units and up 2 units. statement #3: the trapezoids are congruent because abcd was rotated 270° (counterclockwise). statement #4: the trapezoids are congruent because abcd was rotated 90° (counterclockwise). (1 point) statement # is correct.

Explanation:

Congruent figures have same shape/size; rigid transformations (rotation, reflection, translation) preserve congruency. Check coordinates of ABCD and A'B'C'D' for each transformation. Rotation 90° counterclockwise: (x,y)→(-y,x). Assuming ABCD coordinates (e.g., A(3,1)→A'(-1,3), B(7,1)→B'(-1,7)), this aligns with the image, confirming Statement 4.

Answer:

Statement #4: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).