# Lesson Notes 6.3 and

```Lesson Notes 6.3 Proving that a Quadrilateral is a Parallelogram
To prove a quadrilateral is a parallelogram, one of the following must be true:
If this is true
diagram
algebra
Theorem 6-5
Opposite sides are
congruent
WX  ZY and XY  WZ
Then WXYZ is a
parallelogram
W  Y and X  Z
Then WXYZ is a
parallelogram
XE  EZ and WE  EY
Then WXYZ is a
parallelogram
Theorem 6-6
Opposite angles are
congruent
Theorem 6-7
Diagonals bisect each
other
Theorem 6-8
One pair of opposite
sides is both
congruent and parallel
XW = YZ and XW || YZ
Then WXYZ is a
parallelogram
OR
XY = WZ and XY || WZ
Then WXYZ is a
parallelogram
State whether the information given about quadrilateral SMTP is sufficient to prove that it is a parallelogram.
1.
2.
3.
4.
5.
6.
13.
14.
15.
16.
17.
18.
19.
20.
Algebra Find the values of x and y for which the figure must be a parallelogram.
7.
8.
9.
Algebra Find the value of x. Then tell whether the figure must be a parallelogram. Explain your answer.
10.
11.
12.
```