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

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Presentation transcript:

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

Methods of Proving a quadrilateral is a Rectangle 1.Show that both pairs of opposite sides are parallel and that adjacent sides are perpendicular forming right angles. - Use slope for 4 sides 2.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. 4.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 **

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

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