Question 844597
It is always true.
A parallelogram is a quadrilateral where opposite sides are parallel.
So a quadrilateral ABCD is a parallelogram if and only if AB is parallel to DC,
and BC is parallel to AD.
{{{drawing(300,200,-1,5,-1,3,
line(0,0,1,2),line(0,0,3,0),
line(3,0,4,2),line(1,2,4,2),
locate(0.8,2.2,A),locate(4,2.2,B),
locate(3.1,0.2,C),locate(-0.2,0.2,D)
)}}}
The angles between side AB and adjacent sides AD and BC are supplementary (their measures add up to {{{180^o}}} .
The angles between side CD and adjacent sides AD and BC are supplementary.
The angles at opposite vertices are congruent.
There are only two interior angle measures for a parallelogram, and those two angle measures add up {{{180^o}}} .
In the figure above,
the angles at A and C are a pair congruent angles (they have the same measure);
the angles at B and D are another pair of congruent angles,
and any angle of one of those pairs is supplementary to any angle from the other pair.
If all the angles in a parallelogram have the same measure, they all measure {{{90^o}}} , and the parallelogram is a rectangle, which is a special kind of parallelogram.