To prove that the diagonals of a parallelogram are congruent, that parallelogram must be a rectangle. Given: ABCD is a parallelogram with AB parallel to CD and AD parallel to BC. Diagonal AC is congruent to diagonal BD. Prove: ABCD is a rectangle (Angels A, B, C and D right angles). Fill in the blanks: I know __ is congruent to ___ because it's the same segment. I know ___ is congruent to ___ because it's given. I know ___ is congruent to ___ because ___ is a parallelogram (given) and opposite sides of a parallelogram are congruent. Because ___ is congruent to ___, ___ is congruent to ___, and ___ is congruent to , by the side-side-side triangle congruence theorem triangles ___ and ___ are congruent. Angle ___ is congruent to angle ___ because they are corresponding parts of two congruent triangles. Angles __ and ___ are right angles because they're congruent and supplementary (because they are adjacent in a parallelogram). Congruent supplementary angles must be right angles. Opposite angles in a parallelogram are congruent, so if angles ___ and ___ are right angles, then angles ___ and ___ must be, too. I know ___ is a rectangle because angles ___, ___, ___, and ___ are all right angles, and a quadrilateral with four right angle is a rectangle.