1. Tests for Parallelograms
Lesson 6-2
Tests for Parallelograms

2. Proving Quadrilaterals as Parallelograms
Theorem 1:
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram . H G
Theorem 2: E F
If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram .

3. Theorem:
Theorem 3:
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. G H
then Quad. EFGH is a parallelogram. M
Theorem 4: E F
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram .
then Quad. EFGH is a parallelogram.
EM = GM and HM = FM

4. 5 ways to prove that a quadrilateral is a parallelogram.
1. Show that both pairs of opposite sides are || . [definition]
2. Show that both pairs of opposite sides are  .
3. Show that one pair of opposite sides are both  and || .
4. Show that both pairs of opposite angles are  .
5. Show that the diagonals bisect each other .

5. Examples ……
Example 1:
Find the value of x and y that ensures the quadrilateral is a parallelogram.
y+2
6x = 4x+8
2x = 8
x = 4 units
2y = y+2
y = 2 unit 6x
4x+8 2y
Find the value of x and y that ensure the quadrilateral is a parallelogram.
Example 2:
2x + 8 = 120
2x = 112
x = 56 units
5y = 180
5y = 60
y = 12 units
(2x + 8)°
120°
5y°

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7. Thanks for coming!