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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.
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