Opposite angles/sides are equal.
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The simple answer is no, not all parallelograms have at least one right angle. However, there are some that do. Rectangles and squares are 'special' parallelograms that all have at least one right angle.
Diagonals are congruent
The transitive property is if angle A is congruent to angle B and angle B is congruent to angle C, then angle A is congruent to angle C.
Most do, but a square or rectangle is a special case and has all right angles.
The Symmetric Property of Congruence: If angle A is congruent to angle B, then angle B is congruent to angle A. If X is congruent to Y then Y is congruent to X.