Question

in a proof that the diagonals of rectangle abcd are congruent, which statement comes just after the statements that (overline{ad} cong overline{bc}), (overline{ab} cong overline{ab}), and (angle dab cong angle cba)? (1 point) (\bigcirc \triangle dab cong \triangle dao) (\bigcirc \triangle dab cong \triangle aob) (\bigcirc \triangle dab cong \triangle doc) (\bigcirc \triangle dab cong \triangle cba)

Explanation:

To prove the diagonals of a rectangle are congruent, we use triangle congruence. We have \( \overline{AD} \cong \overline{BC} \) (opposite sides of a rectangle), \( \overline{AB} \cong \overline{AB} \) (common side), and \( \angle DAB \cong \angle CBA \) (both right angles in a rectangle). By the SAS (Side - Angle - Side) congruence criterion, we can conclude that \( \triangle DAB \cong \triangle CBA \). The other options do not have the correct corresponding parts to form a congruent triangle with \( \triangle DAB \) based on the given information.

Answer:

D. \( \triangle DAB \cong \triangle CBA \)