5.5 Properties of Parallelograms
Parallelogram Opposite Angles Conjecture (OA)
The opposite angles of a parallelogram are _________________.
D
C
B
A
Parallelogram Consecutive Angles Conjecture (CA)
The consecutive angles of a parallelogram are ____________________.
D
C
B
A
Parallelogram Opposite Sides Conjecture (OS)
The opposite sides of a parallelogram are __________________.
D
C
B
A
Parallelogram Diagonals Conjecture
The diagonals of a parallelogram ______________________.
D
C
E
A
B
Geometry Lesson 5.5: Properties of Parallelograms
Page 1
Example 1: Find the missing measures. (All figures are parallelograms.)
34 cm
50
e
16 cm
a
d
c
b
a = ________
b = ________
68
c = ________
D
5 in
i
f
C
5 cm
3 cm
f = _______
g = _______
h
e = _______
E
14 in
g
d = ________
A
h = _______
EC = _______
i = _______
AC = _______
j = _______
EB = _______
j
Geometry Lesson 5.5: Properties of Parallelograms
B
DB = _______
Page 2
Example 2: Find the perimeter of each parallelogram and triangle.
x+5
I
H
12 cm
x-3
F
G
D
P∆DEC = ___________ P∆ADB = ___________
C
AD = 16 cm
DC = 19 cm
AC = 24 cm
BD = 20 cm
E
A
PFGHI = _____________
P∆DEA = ___________ P∆BDC = ___________
B
P∆AEB = ___________ P∆ABC = ___________
PABCD = _____________
Geometry Lesson 5.5: Properties of Parallelograms
P∆BEC = ___________ P∆DAC = ___________
Page 3
Example 3: Find the missing measures. (All figures are parallelograms.)
c
b
a
d
55
k
18
l
h
126
i
f
e
5 in
D
b = ________
c = _______
d = ________
88
j
m
a = _______
e = _______
f = ________
g = _______
h = _______
i = ________
j = _______
k = _______
l = ________
m = _______
x = ________
y = _________
32
g
C
(5 - x) in
4 in
A
(9 - 2y) in
B
Geometry Lesson 5.5: Properties of Parallelograms
Page 4
Example 4: Find the value of x in each. (All figures are parallelograms).
x
(17x)
x = __________
(3x - 20)
(17x)
x
(5x)
x = __________
(4x - 90)
(5x)
x
(8x)
x = __________
(5x - 80)
(8x)
Example 5: Find x and y in each parallelogram.
(x + 81)
(x + 90)
(4x)
x = ______
y
y = ________
Geometry Lesson 5.5: Properties of Parallelograms
(8x)
x = ______
y
y = ________
Page 5
Example 6: Find x, y, and z in each parallelogram.
38
128
x = ________
y
z
x
y = ________
z = ________
24
106
x = ________
y = ________
z
25
y
x
z = ________
114
x = ________
y = ________
z
y
z = ________
x
Homework: pp. 281 – 283 => 1 – 6; 15 – 18
Geometry Lesson 5.5: Properties of Parallelograms
Page 6