PARALLELOGRAMS
In this lesson you will explore:
The definition of a parallelogram.
Special characteristics of
parallelograms.
How to apply the characteristics of
parallelograms to solve problems.
Common Core Standards: N-Q.1, N-Q.2, N-Q.3, G-CO.11, G-GPE.4, G-GPE.5
PARALLELOGRAM - Definition
A parallelogram is a quadrilateral with BOTH
pairs of opposite sides parallel.
Naming Parallelograms
We use a small parallelogram like
when naming a parallelogram.
TEAM
prior to the vertices
Naming Parallelograms
Practice naming the following parallelograms.
Examples
*Images courtesy of Microsoft
If a quadrilateral is a parallelogram then its
opposite sides are congruent.
If a quadrilateral is a parallelogram then its
opposite angles are congruent.
If a quadrilateral is a parallelogram then its
consecutive angles are supplementary.
Consecutive supplementary angle sets.
SET 1
SET 1
SET 2
SET 3
SET 4
If a quadrilateral is a parallelogram then its
diagonals bisect each other.
Example 1: ACES is a parallelogram.
Find the unknown lengths.
a. CE = 6m
b. FE = 7m
c. AE = 14m
Example 2: In parallelogram ABCD,
m<C = 105o. Find each angle measure.
a. m<A = 105o
A
D
105o
75o
75o
105o
b. m<D = 75o
B
m<B + m<C = 180o
m<B + 105o = 180o
- 105o -105o
m<B = 75o
C
Example 3: WXYZ is a parallelogram. Find the
value of x.
W
X
(3x + 18)o
Z
(4x - 9)o
Y
3x + 18 = 4x – 9
-3x
-3x
18 = x – 9
+9
+9
27 = x
Example 4: A four sided concrete slab has
consecutive angle measures of 85o, 94o, 85o, and
96o. Is the slab a parallelogram? Explain.
96o
85o
85o
94o
No.
If the quadrilateral was a parallelogram, both pairs
of opposite angles would be congruent.
PARALLELOGRAMS
In this lesson you learned:
A parallelogram is a quadrilateral with both pairs
of opposite sides parallel.
Parallelograms have special characteristics like:
Both pairs of opposite angles are congruent.
Both pairs of opposite sides are congruent.
Consecutive angles are supplementary.
The diagonals bisect each other.
How to apply the characteristics of parallelograms
to solve problems.