1. Lesson 6-2
Parallelograms

2. Parallelogram Definition:
4/28/2017
Parallelogram
Definition:
A quadrilateral whose opposite sides are parallel. C B A D
Naming:
A parallelogram is named using all four vertices.
You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction.
For example, this can be either ABCD or ADCB.

3. Properties of ParallelogramB
Properties of Parallelogram P D C
1. The opposite sides are congruent.
2. The opposite angles are congruent.
3. Each pair of consecutive angles is supplementary.
4. Diagonals bisect each other.
P is the midpoint of

4. Examples H K M P L Draw HKLP. If HK = _______ and HP = ________ .
m<K = m<______ .
m<L + m<______ = 180.
If m<P = 65, then m<H = ____,m<K = ______ and m<L =____.
Draw in the diagonals. They intersect at M.
If HM = 5, then ML = ____
If KM = 7, then KP = ____
If HL = 15, then ML = ____
If m<HPK = 36, then <PKL = _____ . PL KL P
P or K
115°
115° 65
5 units
14 units
7.5 units 36

5. Proving a Quadrilateral is a Parallelogram
Lesson 6-3
Proving a Quadrilateral is a Parallelogram

6. 5 ways to prove that a quadrilateral is a parallelogram.
1. Show that both pairs of opposite sides are || .
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 .

7. Examples ……
Example 1:
Find the value of x and y that ensure the quadrilateral is a parallelogram. y
6x = 4x+8
2x = 8
x = 4
y² = y (y *y = y)
y = 1 6x
4x+8 y²
Find the value of x and y that ensure the quadrilateral is a parallelogram.
Example 2:
2x + 8 = 120
2x = 112
x = 56
5y = 180
5y = 60
y = 12
(2x + 8)°
120°
5y°