6.2 & 6.3 - PARALLELOGRAMS
QUADRILATERAL:
a)
b)
PARALLELOGRAM:
EXAMPLE 1:
N
P
a) The parallelogram at the right
has four vertices. They are
M
_________________________
Q
b) It would be NAMED:_____________________
c) The OPPOSITE SIDES of
d) The OPPOSITE ANGLES of
MNPQ are ____________________
MNPQ are __________________
e) The CONSECUTIVE ANGLES of
MNPQ are _______________
______________________________________________________
N
P
Q
M
Using
MNPQ, what conjectures can you make about the following:
a) OPPOSITE SIDES
 ___________________________________________________
 ___________________________________________________
b) OPPOSITE ANGLES
 ___________________________________________________
c) CONSECUTIVE ANGLES
 ___________________________________________________
When polygons have more than three sides, they have diagonals.
DIAGONAL:
T
EXAMPLE 2: Name the following.
B
D
T
S
O
G
C
A
C
L
S
O
D
A
S
Vertices:
__________
Name:
__________
Opposite
Vertices:
__________
Vertices:
__________
Name:
__________
Opposite
Vertices:
__________
Vertices:
__________
Name:
__________
Opposite
Vertices:
__________
Vertices:
__________
Name:
__________
Opposite
Vertices:
__________
Diagonals:
__________
Diagonals:
__________
Diagonals:
__________
Diagonals:
__________
BISECT:
Diagonals of a parallelogram bisect each other.
Thus, parallelograms have five properties. They are:
1)_______________________________________________________
2)_______________________________________________________
3)_______________________________________________________
4)_______________________________________________________
5)_______________________________________________________
EXAMPLE 3:
Complete each statement regarding the parallelogram below.
a) Name the parallelogram:__________
D
b) AB  ________
c) DA  ________
d) CDA  ________
e) DE  ________
A
E
C
B
EXAMPLE 4:
If ABCD is a parallelogram, mA = x and mD = (2x – 3), find the
value of ‘x’.
EXAMPLE 5:
XYZW is a parallelogram with diagonals XZ and YW that intersect
at point A. If XA = 3m and ZA = 5m – 4, and YW = 10m, find ‘m’.
MORE EXAMPLES:
For each parallelogram, find the values of ‘x’, ‘y’, and ‘z’.
6.
7.
8.
y
120
z
x
y
80
y
35
x
z
x = ________; y = ________; x = ________; y = ________;
z = ________
z = ________
x
70
z
30
x = ________; y = ________;
z = ________
EXAMPLE 9:
WXYZ is a parallelogram. If mZWX = b and mWXY = d, find
the values of ‘a’, ‘b’, ‘c’, and ‘d’.
X
2c
W
b = ________
15
18
a
Z
31
22
a = ________
c = ________
Y
d = ________