Section 5.6: Proving That A Quadrilateral Is

A ParallelogramBy 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!Given: KYLE is a quadrilateral.KL and YE bisect each other.

Prove: KYLE is a parallelogram.K

Y L

E

P

1. KYLE is a quadrilateral

1. Given

2. KL and YE bisect each other

2. Given

3.KYLE is a parallelogram

3. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

…And Another Sample Problem!B

I R

D5x

3x + 4

x + 74x + 1

Given: BD

IR

Is BIRD a parallelogram?

5x = 3x + 45x-3x= 42x = 4x = 2BI = 4x + 1

BI = 9

DR = x + 7DR = 9 DR BI

Of course it is!If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.

Now Its YOUR Turn!3x + 42

y - 20 5y+ x

B O

ZR

Given: BOZR is a parallelogramFind: <O

Be careful!

What’s the Answer?!?!

y- 20 + 5y+ x = 180x=-6y +2003x + 42= 5y + x2x – 5y = -422(-6y +200) -5y=-42-12y+400 -5y=-42-17y=-442y=26 <O= y –

20<O= 26-20<O= 6

One Last Problem Given: WORD is a parallelogramWO= 7x+17WR= 10x+41RD= 5x+32What is the length of RD?

W O

R D

The Answer7x+17=5x+322x=15x=7.5DO= 69.5

Works CitedAnd 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.