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By Kyle Pitts But what are the ways to prove a quadrilateral is a parallelogram??? There’s a lot of ways!!! If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram TA DA!!! You can also prove it like this: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram Or… If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram But what about this? If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram And.. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Here’s a Sample Problem! 1. KYLE is a quadrilateral 1. Given 2. KL and YE bisect each other 2. Given 3.KYLE is a parallelogram Given: KYLE is a quadrilateral. KL and YE bisect each other. Prove: KYLE is a parallelogram. K E P 3. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram Y L …And Another Sample Problem! B Given: BD 5x D IR Is BIRD a parallelogram? 4x + 1 5x = 3x + 4 5x-3x= 4 2x = 4 x=2 BI = 4x + 1 BI = 9 DR = x + 7 DR = 9 x+7 I DR BI 3x + 4 R Of course it is! If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Now Its YOUR Turn! B Given: BOZR is a parallelogram Find: <O O 3x + 42 Be careful! y - 20 R 5y+ x Z What’s the Answer?!?! y- 20 + 5y+ x = 180 x=-6y +200 3x + 42= 5y + x 2x – 5y = -42 2(-6y +200) -5y=-42 -12y+400 -5y=-42 -17y=-442 y=26 <O= y – 20 <O= 26-20 <O= 6 One Last Problem Given: WORD is a parallelogram WO= 7x+17 WR= 10x+41 RD= 5x+32 What is the length of RD? R W O D The Answer 7x+17=5x+32 2x=15 x=7.5 DO= 69.5 Works Cited And Finally, the most exciting part of the power point, the WORKS CITED!! “Proving That A Quadrilateral Is A Parallelogram.” Geometry for Enjoyment and Challenge. New ed. 1997. Print.