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Geometry Notes Lesson 4.1B Special Quadrilaterals

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Parallelogram Parallelogram – a quadrilateral with two pairs of opposite sides parallel

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Properties of parallelograms Opposite sides are congruent Opposite angles are congruent Diagonals bisect each other

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Rectangle Rectangle – a parallelogram with four right angles

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Special properties of rectangles Diagonals are congruent

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Rhombus Rhombus – a parallelogram with four congruent sides

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Special properties of rhombuses Diagonals are perpendicular Each diagonal bisects opposite angles

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Square Square – a parallelogram with four right angles and four congruent sides

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Special properties of squares Diagonals are congruent Diagonals are perpendicular Each diagonal bisects opposite angles

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Kite Kite – A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

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Special properties of kites. Diagonals bisect 2 of the angles Diagonals are perpendicular One diagonal is bisected

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Trapezoid Trapezoid – A quadrilateral with exactly one pair of parallel sides

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Special properties of trapezoids Same-Side Interior Angles = 180

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Isosceles Trapezoid Isosceles Trapezoid – a trapezoid whose nonparallel sides are congruent

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Special properties of isosceles trapezoids. Nonparallel sides are congruent Base Angles are congruent Diagonals are congruent

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The following is a diagram to show how different quadrilaterals are related.

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True or False? All parallelograms are squares. False! Some kites are rectangles. False! Some parallelograms are rectangles. True! Some trapezoids are parallelograms. False! All squares are kites. False! All squares are rectangles. True!

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True or False? All parallelograms are kites. All rectangles are squares. Some kites are squares. All kites are quadrilaterals. False! True!

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Name ALL special quadrilaterals that satisfy the following conditions. Both pairs of opposite sides are parallel Diagonals are perpendicular All angles are right angles Parallelogram, rectangle, rhombus, square rhombus, square, kite rectangle, square

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Name ALL special quadrilaterals that satisfy the following conditions. Two pairs of opposite sides are equal All four sides are equal Both pairs of opposite angles are equal Parallelogram, rectangle, rhombus, square rhombus, square Parallelogram, rectangle, rhombus, square

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Name ALL special quadrilaterals that satisfy the following conditions. Diagonals bisect each other Both diagonals are equal Only one pair of sides is parallel All adjacent pairs of angles are supplementary Parallelogram, rectangle, rhombus, square Rectangle, square, Isosceles Trapezoid Trapezoid, Isosceles Trapezoid Parallelogram, rectangle, rhombus, square

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Fill in the Venn Diagram Given labels: Parallelograms, Kites, Rectangles Quadrilaterals Trapezoids SquaresRhombuses

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EXAMPLES Draw a quadrilateral with two pairs of opposite parallel sides on the graph. -5 -2 -3-4 1234 1 2 3 4 5 -2 -3 -4

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Examples Draw a quadrilateral with two pairs of congruent adjacent sides on the graph. -2 -3-4 1234 1 2 3 4 5 -2 -3 -4

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Examples Use the slope and/or distance formulas to determine the MOST PRECISE name for the quadrilateral with the given vertices. A (0, 0); B(5, 5); C(8, 4); D(7, 1)

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Examples Use the slope and/or distance formulas to determine the MOST PRECISE name for the quadrilateral with the given vertices. A(2, 1); B(5, -1); C(4, -4); D(1, -2)

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