Properties of Parallelograms and Related Concepts

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Parallelogram Opposite Sides

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Opposite sides of a parallelogram are congruent. Example: If AB || CD and AD || BC, then AB = CD and AD = BC.

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Parallelogram Opposite Angles

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Opposite angles of a parallelogram are congruent. Example: If ABCD is a parallelogram, then ∠A = ∠C and ∠B = ∠D.

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Parallelogram Consecutive Angles

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Consecutive angles of a parallelogram are supplementary. Example: If ABCD is a parallelogram, then ∠A + ∠B = 180°.

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Parallelogram Diagonals

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Diagonals of a parallelogram bisect each other. Example: If AC and BD are diagonals, then AO = OC and BO = OD.

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Rectangle Properties

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A rectangle has all properties of a parallelogram, plus congruent diagonals and four right angles. Example: If ABCD is a rectangle, then ∠A = ∠B = ∠C = ∠D = 90° and AC = BD.

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Rhombus Properties

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A rhombus has all properties of a parallelogram, plus all sides congruent and diagonals perpendicular. Example: If ABCD is a rhombus, then AB = BC = CD = DA and AC ⊥ BD.

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Square Properties

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A square has all properties of a rectangle and rhombus, making it a regular quadrilateral. Example: If ABCD is a square, then all sides and angles are equal, and AC = BD.

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Distance Formula

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Slope Formula

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Midpoint Formula

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