In parallelogram ABCD, several key properties and relationships exist:
Opposite sides are parallel and congruent. This means AB || CD and AD || BC, and AB = CD and AD = BC.
Opposite angles are congruent. This means ∠A = ∠C and ∠B = ∠D.
Consecutive angles (angles that share a side) are supplementary, meaning they add up to 180 degrees. For example, ∠A + ∠B = 180°, ∠B + ∠C = 180°, ∠C + ∠D = 180°, and ∠D + ∠A = 180°.
The diagonals bisect each other. This means that the point where the diagonals intersect (let's call it E) is the midpoint of both diagonals AC and BD. Therefore, AE = EC and BE = ED. The diagonals themselves are not necessarily congruent unless the parallelogram is also a rectangle.
The area of a parallelogram can be calculated as base * height (Area = b * h), where the height is the perpendicular distance between the base and its opposite side. Also, it can be calculate as |AB|*|AD|*sin(∠A).
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