Question

trapezoid abcd was transformed to produce trapezoid abcd.
which statement justifies why the two figures are congruent?
a. by definition, transformations always produce congruent figures.
b. the transformations applied to trapezoid abcd were not rigid transformations.
c. the transformations applied to trapezoid abcd were rigid transformations.
d. trapezoid abcd was dilated to produce trapezoid abcd.

Explanation:

• Option A is incorrect because not all transformations (e.g., dilation) produce congruent figures.
• Option B is incorrect as rigid transformations (like rotation, reflection, translation) preserve congruence, and if the transformations were non - rigid, the figures wouldn't be congruent.
• Option C is correct. Rigid transformations (translation, rotation, reflection) do not change the shape or size of a figure, so they preserve congruence.
• Option D is incorrect because dilation changes the size of a figure, and if a dilation was applied, the trapezoids wouldn't be congruent.

Answer:

C. The transformations applied to trapezoid ABCD were rigid transformations.