### Section 5.6: Proving That A Quadrilateral Is A Parallelogram

```By Kyle Pitts
But what are the ways to prove a
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
congruent, then the
parallelogram
Or…
If one pair of opposite sides of a
congruent, then the quadrilateral is a
parallelogram
 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is
a parallelogram
And..
If both pairs of opposite angles of a
Here’s a Sample Problem!
1. KYLE is a
1. Given
2. KL and YE
bisect each
other
2. Given
3.KYLE is a
parallelogram
Given: KYLE is a
KL and YE bisect
each other.
Prove: KYLE is a
parallelogram.
K
E
P
3. If the diagonals of 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
B
Given: BOZR is a
parallelogram
Find: <O
O
3x + 42
Be careful!
y - 20
R
5y+ x
Z
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