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Rectangle Proofs

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

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Rectangle Proofs

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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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