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Quadrilaterals

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Heather Juel

on 7 March 2011

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Transcript of Quadrilaterals

Quadrilaterals By: Heather Juel Parallelogram a quadrilateral with two pairs of parallel sides Classified as a quadrilateral and a parallelogram Properties of Parallelograms Theorem 6-2-1 if a quadrilateral is a parallelogram, then its opposite sides are congruent Theorem 6-2-2 if a quadrilateral is a parallelogram, then its opposite angles are congruent Theorem 6-2-3 if a quadrilateral is a parallelogram, then its consecutive angles are supplementary Theorem 6-2-4 if a quadrilateral is a parallelogram, then its diagonals bisect each other Conditions for Parallelograms Theorem 6-3-1 if one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram Theorem 6-3-2 if both pairs of oppostite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram Theorem 6-3-3 if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Theorem 6-3-4 if an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram Theorem 6-3-5 if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a paralleogram Rectangle a quadrilateral with four right angles Classified as a quadrilateral, a parallelogram and a rectangle Properties of Rectangles if a quadrilateral is a parallelogram, then its opposite sides are congruent Theorem 6-2-1 Theorem 6-2-3 if a quadrilateral is a parallelogram, then its consecutive angles are supplementary if a quadrilateral is a parallelogram, then its diagonals bisect each other Theorem 6-2-4 Conditions for Rectangles Theorem 6-4-1 if a quadrilateral is a rectangle, then it is a parallelogram Theorem 6-4-2 if a parallelogram is a rectangle, then its diagonals are congruent Theorem 6-3-1 if one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram Theorem 6-3-2 if both pairs of oppostite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram Theorem 6-3-3 if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Theorem 6-3-4 if an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram Theorem 6-3-5 if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram if one angle of a parallelogram is a right angle, then the parallelogram is a rectangle Theorem 6-5-1 Theorem 6-5-2 if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle Rhombus a quadrilateral with four congruent sides classified as a quadrilateral, a parallelogram and a rhombus if a quadrilateral is a parallelogram, then its diagonals bisect each other Theorem 6-2-2 if a quadrilateral is a parallelogram, then its consecutive angles are supplementary Theorem 6-2-3 if a quadrilateral is a parallelogram, then its opposite angles are congruent Theorem 6-2-4 if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a paralleogram if both pairs of oppostite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram Theorem 6-3-5 if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Theorem 6-3-2 if an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram Theorem 6-3-3 Theorem 6-3-1 if one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram Theorem 6-3-4 Properties of Rhombi if a quadrilateral is a rhombus, then its diagonals are perpendicular Conditions for Rhombi Theorem 6-5-3 if one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus Theorem 6-5-4 Theorem 6-5-5 if one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus Square a quadrilateral with four right angles and four congruent sides classified as a quadrilateral, a parallelogram, a rectangle and a rhombus Properties of Squares if a quadrilateral is a parallelogram, then its opposite sides are congruent Theorem 6-2-1 Theorem 6-2-1 if a quadrilateral is a parallelogram, then its opposite sides are congruent Theorem 6-2-2 if a quadrilateral is a parallelogram, then its opposite angles are congruent if a quadrilateral is a parallelogram, then its opposite angles are congruent Theorem 6-2-2 if a quadrilateral is a parallelogram, then its diagonals bisect each other if a quadrilateral is a parallelogram, then its consecutive angles are supplementary Theorem 6-2-4 Theorem 6-2-3 if a parallelogram is a rectangle, then its diagonals are congruent Theorem 6-4-2 if a quadrilateral is a rectangle, then it is a parallelogram Theorem 6-4-1 Theorem 6-4-3 if a quadrilateral is a rhombus, then it is a parallelogram Theorem 6-4-4 Theorem 6-4-5 if a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles if a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles Theorem 6-4-5 if a quadrilateral is a rhombus, then it is a parallelogram Theorem 6-4-3 Theorem 6-4-4 if a quadrilateral is a rhombus, then its diagonals are perpendicular if one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram Theorem 6-3-5 Theorem 6-3-4 Theorem 6-3-2 if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Theorem 6-3-3 if an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram if both pairs of oppostite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a paralleogram Theorem 6-3-1 Conditions for Squares if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle if one angle of a parallelogram is a right angle, then the parallelogram is a rectangle Theorem 6-5-2 Theorem 6-5-1 if one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus Theorem 6-5-5 if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus if one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus Theorem 6-5-4 Theorem 6-5-3 Kite a quadrilateral with exactly two pairs of congruent consecutive sides classified as a quadrilateral and a kite Properties of Kites Theorem 6-6-1 if a quadrilateral is a kite, then its diagonals are perpendicular if a quadrilateral is a kite, then exactly one pair of opposite angles are congruent Theorem 6-6-2 Trapezoid a quadrilateral with exactly one pair of parallel sides classified as a quadrilateral and a trapezoid Properties and Conditions of Isosceles Trapezoids Theorem 6-6-3 if a quadrilaterral is a isosceles trapezoid, then each pair of base angles are congruent Theorem 6-6-4 if a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles a trapeziod is isosceles if and only if its diagonals are congruent Theorem 6-6-5 The End
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