Properties of Quadrilaterals

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Exported from a quizlet made by messygoat.

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90 Terms

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Properties of Parallelograms

  1. Opposite sides parallel

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  1. Opposite sides congruent

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  1. Opposite angles congruent

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  1. Diagonals bisect each other

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  1. Any pair of consecutive angles are supplementary

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Properties of Rectangles

  1. All of the properties of a parallelogram, plus

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  1. All angles are right angles

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  1. Diagonals are congruent

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Properties of Kites

  1. Two disjoint pairs of consecutive sides are congruent

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  1. Diagonals are perpendicular to each other

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  1. ONE diagonal is the perpendicular bisector of the other

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  1. ONE diagonal bisects a pair of opposite angles

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  1. ONE pair of opposite angles congruent

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Properties of Rhombuses

  1. All of the properties of a parallelogram, plus

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  1. All of the properties of a kite, plus

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  1. All sides are congruent (i.e. it is equilateral)

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  1. Diagonals bisect all of the angles

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  1. Diagonals are perpendicular bisectors of each other

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  1. Diagonals divide the rhombus into four congruent right triangles.

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Properties of Squares

  1. All of the properties of a rectangle, plus

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  1. All of the properties of a rhombus, plus

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  1. Diagonals form four congruent isosceles right triangles

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Properties of Isosceles Trapezoids

  1. Legs are congruent by definition

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  1. Bases are parallel (exactly ONE set of parallel lines)

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  1. Lower base angles are congruent

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  1. Upper base angles are congruent

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  1. Diagonals are congruent

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  1. Any lower base angle is supplementary to any upper base angle

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Opposite sides parallel

Parallelogram

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Rectangle

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Rhombus

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Square

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Trapezoid (only ONE set)

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Opposite sides congruent

Parallelogram

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Rectangle

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Rhombus

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Square

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Isosceles Trapezoid (only ONE set: legs)

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Opposite angles congruent

Parallelogram

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Rectangle

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Rhombus

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Square

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Kite (only ONE set)

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Diagonals bisect each other

Parallelogram

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Rectangle

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Rhombus

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Square

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Kite (only ONE diagonal is bisected)

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Any pair of consecutive angles are supplementary

Parallelogram

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Rectangle

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Rhombus

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Square

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All angles are right angles

Rectangle

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Square

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Diagonals are congruent

Rectangle

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Square

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Isosceles Trapezoid

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Two disjoint pairs of consecutive sides are congruent

Kite

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Rhombus

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Square

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Diagonals are perpendicular to each other

Kite

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Rhombus

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Square

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One diagonal is perpendicular bisector of the other

Kite

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Rhombus (true for both diagonals)

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Square (true for both diagonals)

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One diagonal bisects a pair of opposite angles

Kite

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Rhombus (true for both diagonals)

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Square (true for both diagonals)

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One pair of opposite angles congruent

Kite

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Rhombus (true for both pairs)

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Square (true for both pairs)

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Diagonals are perpendicular bisectors of each other

Rhombus

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Square

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Diagonals bisect opposite angles

Rhombus

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Square

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Two pairs opposite angles congruent

Rhombus

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Square

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Rectangle

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All sides congruent (equilateral)

Rhombus

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Square

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Diagonals divide the quadrilateral into 4 congruent right triangles

Rhombus

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Square

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Diagonals form four congruent isosceles right triangles

Square

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Legs are congruent

Isosceles Trapezoid

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Bases are parallel

Trapezoid

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Isosceles Trapezoid

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Lower base angles are congruent

Isosceles Trapezoid

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Upper base angles are congruent

Isosceles Trapezoid

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Any lower base angle is supplementary to any upper base angle

Isosceles Trapezoid