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Proving Quadrilaterals Are Rectangles: Methods and Examples

This guide outlines the methods for proving that a quadrilateral is a rectangle. A rectangle is defined as a parallelogram with four right angles and equal diagonals. To validate a quadrilateral as a rectangle, you can demonstrate that both pairs of opposite sides are parallel and adjacent sides are perpendicular by using slope, or show that opposite sides and diagonals are equal using distance formulas. Each proof should conclude with a statement affirming the quadrilateral's properties. Practice by proving given quadrilaterals using different methods.

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Proving Quadrilaterals Are Rectangles: Methods and Examples

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  1. Rectangle Proofs A rectangle is a parallelogram with four right angles and congruent diagonals.

  2. Methods of Proving a quadrilateral is a Rectangle • Show that both pairs of opposite sides are parallel and that adjacent sides are perpendicular forming right angles. - Use slope for 4 sides • Show that both pairs of opposite sides are equal and diagonals are equal. • Use distance for 4 sides and 2 diagonals

  3. First prove the quadrilateral is a parallelogram using any of the 4 methods and then show that the diagonals are equal using the distance 2 times. • First prove the quadrilateral is a parallelogram using any of the 4 methods and then show that the parallelogram has a right angle by using the slope of 2 adjacent sides. ** Be sure to include a concluding statement with each method of proof **

  4. Example Prove the following quadrilateral is a rectangle • J( 1 , 3 ) K( -3 , 6 ) L( -9 , -2 ) M( -5 , -5 )

  5. HOMEWORK:Prove each of the following quadrilaterals are Rectangles Use a different method for each of the first 3 proofs. Ex. • A( 0 , 2) B( 4 , 8 ) C( 7 , 6 ) D( 3 , 0 ) • P( 0 , 5 ) Q( 3 , 4 ) R( 0 , -5 ) S( -3, -4 ) • M( -2 , 1 ) A( -1 , 4 ) T( 8 , 1 ) H( 7 , -2 ) • J( 0 , 0 ) K( a , 0 ) L( a , b ) M( 0 , b )

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