Parallelogram: opposite angles equal

Dependencies: theorem Parallel ⇒ alternate angles equal (Parallel ⇒ alternate angles equal, B.06).

Statement

Let quadrilateral $ABCD$ be a parallelogram, i.e. $AB \parallel CD$ and $AD \parallel BC$. Then its two pairs of opposite angles are equal:

Here $\angle A$ denotes the interior angle at vertex $A$ subtended by the two adjacent sides $AD$ and $AB$, namely $\angle DAB$; the other three interior angles $\angle B = \angle ABC$, $\angle C = \angle BCD$, $\angle D = \angle CDA$ are defined similarly.