1. ParallelogramsParallelograms
You will learn to identify and use the properties of
parallelograms.
1) Parallelogram

2. ParallelogramsParallelograms
A parallelogram is a quadrilateral with two pairs of ____________.parallel sides
A B
D C
In parallelogram ABCD below, andCBDA || DCAB ||
Also, the parallel sides are _________.congruent
Knowledge gained about “parallels” (chapter 4)
will now be used in the following theorems.

3. Theorem
8-2
Theorem
8-3
Theorem
8-4
ParallelogramsParallelograms
Opposite angles of a
parallelogram are
________.
Opposite sides of a
parallelogram are
________.
The consecutive
angles of a
parallelogram are
____________.
A B
D C
A B
D C
A B
D C
A  C and B  D
DCABCBDA ||and,||
mA + mB = 180
mD + mC = 180
congruent
congruent
supplementary

4. ParallelogramsParallelograms
In RSTU, RS = 45, ST = 70, and U = 68.
R
U
S
T
45
70
68°
Find:
RU = ____
UT = _____
mS = _____
mT = _____
70 Theorem 8-3
45 Theorem 8-3
68° Theorem 8-2
112° Theorem 8-4

5. ParallelogramsParallelograms
Theorem
8-5
The diagonals of a parallelogram ______ each other.
A
D
B
C
E
bisect
ECAE ≅
EBDE ≅
In RSTU, if RT = 56, find RE.
R
U
S
T
E
RE = 28
( )RTRE
2
1
=
( )56RE
2
1
=

6. A
D
B
C
ParallelogramsParallelograms
In the figure below, ABCD is a parallelogram.
DB  BD
Since AD || BC and
diagonal DB is a transversal,
then ADB  CBD.
(Alternate Interior angles)
Since AB || DC and
diagonal DB is a transversal,
then BDC  DBA.
(Alternate Interior angles)
BDCDBA ∆≅∆
ASA Theorem

7. ParallelogramsParallelograms
Theorem
8-6
A diagonal of a parallelogram separates it into two
_________________.
A
D
B
C
congruent triangles
BDCDBA ∆≅∆

8. ParallelogramsParallelograms
The Escher design below is based on
a _____________.
You can use a parallelogram to make a simple
Escher-like drawing.
Change one side of the parallelogram and then
translate (slide) the change to the opposite side.
The resulting figure is used to make a design
with different colors and textures.
parallelogram

9. ParallelogramsParallelograms

10. ParallelogramsParallelograms