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parallelogram
both pairs of opposite sides are parallel, both pairs of opposite angles are congruent, all consecutive angles are supplementary, diagonals bisect eachother, and one pair of opposite sides is both congruent and parallel
rectangle
EVERYTHING FROM A PARALLELOGRAM, all four interior angles are right angles, and all diagonals are congruent
rhombus
EVERYTHING FROM A PARALLELOGRAM, all four sides are congruent, the diagonals are perpendicular, all diagonals bisect opposite angles
square
EVERYTHING FROM A PARALLELOGRAM, all four sides are congruent, all four angles are right angles, the diagonals are congruent AND perpendicular, the diagonals bisect opposite angles
trapezoid
bases are parallel
isosceles trapezoid
bases are parallel, legs are congruent, diag are congruent, base angles are congruent