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Published byTerence Smith Modified over 8 years ago

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Advanced Geometry 5.4 / 5 Four Sided Polygons /
Properties of Quadrilaterals Learner Objective: I will solve problems using properties
of special quadrilaterals.

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Polygon Plane Figure Consists only of segments Consecutive sides intersect only at endpoints Non-Consecutive sides do not intersect Each vertex belongs to exactly two sides Convex Polygon A polygon in which each interior angle has a measure less than 180. Concave Polygon A polygon in which at least one interior angle has a measure greater
than 180. Diagonal of a Polygon Any segment that connects two nonconsecutive (nonadjacent)
vertices of the polygon is a Diagonal of the Polygon.

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**Quadrilateral: A four sided Polygon**

Special Quadrilaterals Parallelogram: Definition: A Parallelogram is a Quadrilateral in which both pairs of
opposite sides are parallel. Properties: Opposite sides are congruent Opposite angles are congruent Diagonals bisect each other Any pair of consecutive angles are supplementary

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Rectangle: Definition: A Rectangle is a Parallelogram in which at least one angle is a
right angle. Properties: All properties of a Parallelogram apply by definition All angles are right angles The diagonals are congruent

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Rhombus: Definition: A Rhombus is a Parallelogram in which at least two consecutive
sides are congruent. Properties: All properties of a Parallelogram apply by definition All sides are congruent Diagonals are perpendicular bisectors of each other Diagonals bisect the angles Diagonals divide the rhombus into four congruent right triangles

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Square: Definition: A Square is a Parallelogram that is both a Rectangle and a
Rhombus. Properties: All properties of a rectangle apply by definition All properties of a rhombus apply by definition The diagonals form four isosceles right triangles (45⁰-45⁰-90⁰)

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Kite: Definition: A Kite is a quadrilateral in which two disjoint pairs of consecutive
sides are congruent. Properties: Diagonals are perpendicular One diagonal is the perpendicular bisector of the other One diagonal bisects a pair of opposite angles One pair of opposite angles are congruent

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Trapezoid: Definition: A Trapezoid is a quadrilateral with exactly one pair of parallel
sides. The parallel sides are called bases of the trapezoid.

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Isosceles Trapezoid: Definition: An Isosceles Trapezoid is a trapezoid in which the nonparallel
sides (legs) are congruent. Properties: Legs congruent by definition Bases parallel by definition Lower base angles congruent Upper base angles congruent Diagonals are congruent Any lower base angle is supplementary to any upper base angle

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**_______ rhombuses are squares _______ squares are rhombuses **

quadrilateral parallelogram trapezoid isosceles trapezoid rectangle square rhombus kite kite kite Some All No _______ rhombuses are squares _______ squares are rhombuses _______ rhombuses are kites _______ trapezoids are rectangles _______ rectangles are parallelograms _______ kites are rhombuses _______ trapezoids are parallelograms _______ rectangles are rhombuses _______ squares are rectangles _______ parallelograms are quadrilaterals _______ isosceles trapezoids are parallelograms

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STATEMENTS REASONS

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