# Geometry Notes 6.3 Conditions for Parallelograms 1.

```Geometry
Notes 6.3
Conditions for Parallelograms
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&quot;then the quadrilateral is a parallelogram.
Determine whether or not enough information is given to determine the quadrilateral is a
parallelogram. If yes, state the reason.
a.)
b.)
c.)
d.)
e.)
f.)
120&deg;
60&deg;
60&deg;
Example 1: What value of x and y will make the quadrilateral a parallelogram?
x + 3y
20
5y
2(x + y - 1)
Example 2: What value of x and y will make the quadrilateral a parallelogram?
(3 x + 5) &deg;
(2 x)&deg;
Example 3: Show that PQRS is a parallelogram for a = 2.4 and b = 9.
Example 4: Prove ABCD is a parallelogram.
A (2, -1)
B (1, 3)
C (6, 5)
D (7, 1)
STEP 1: Graph the parallelogram
STEP 2: Choose a technique:
• opposite sides ||
• opposite sides ≅
• one pair of opposite
sides ≅ and ||
STEP 3: Choose a formula:
• slope formula
• distance formula
STEP 4: Do the algebra!!!
70 &deg;
(x + 3y) &deg;
```