Step-by-step explanation:
Consider a parallelogram ABCD. By definition of a parallelogram, opposite sides are parallel, so AB || CD and BC || AD.
That means that ∠A and ∠B are consecutive interior angles, and ∠B and ∠C are also consecutive interior angles.
Therefore, ∠A and ∠B are supplementary, and ∠B and ∠C are supplementary:
∠A + ∠B = 180
∠B + ∠C = 180
Subtract the two equations:
∠A − ∠C = 0
∠A = ∠C
Therefore, opposite angles in a parallelogram are congruent.
