Final answer:
The angle congruent to ∠BIR in trapezoid FROG after dilation is ∠FIE, according to the properties of dilation which preserve angle measures in similar figures.
Step-by-step explanation:
The student's question is about identifying a congruent angle after a dilation transformation has occurred between two geometric figures, specifically trapezoids. The dilation of trapezoid BIRD to form trapezoid FROG means that corresponding angles remain congruent. Since the student is asked which angle corresponds to ∠BIR in trapezoid FROG, we can use the properties of dilation, which state that corresponding angles in similar figures are congruent. Therefore, since ∠BIR is an angle at vertex I, the corresponding angle must be at the vertex that corresponds to I in trapezoid FROG, which is ∠FIE.
The explanation reveals that the corresponding angle in trapezoid FROG is ∠FIE, which is answer choice (c). This conclusion is based on the fact that dilation preserves angle measure, therefore corresponding angles in similar figures such as the two trapezoids in question are congruent.