Complete the proof that a parallelogram whose diagonals are congruent has a right angle. D 1 2 3 4 This proof uses this theorem: Opposite sides in a parallelogram are congruent. 5 6 7 4 8 9 Statement AB AD BC AB DC AD DA AC DB CD and E ABAD ADCB m41=m43 m/1+m/4 = 180 2 m/1 180 m/1 = 90 3 B Reason Given C Opposite sides in a parallelogram are congruent. (1) Line segments are congruent to themselves. Given Side-side-side congruence (2,3,4) Corresponding parts of congruent triangles are congruent. (5) When a transversal crosses parallel lines, same-side interior angles sum up to 180. (1) Substitute (6,7) Divide both sides by 2 (8)