Transcript 6.2 Properties of Parallelograms

6.2 PROPERTIES OF
PARALLELOGRAMS
OBJECTIVES:
• Prove and apply properties of
parallelograms.
• Use properties of parallelograms to
solve problems.
6.2 PROPERTIES OF PARALLELOGRAMS
A
Parallelogram ABCD: (
1.
2.
3.
4.
5.
B
ABCD):
D
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary
The diagonals bisect each other.
C
6.2 PROPERTIES OF PARALLELOGRAMS
Example 1:
In
CDEF, DE = 74 mm, DG = 31 mm
and mFCD = 42. Find:
a) CF
C
b) DF
c) mEFC
D
E
G
F
6.2 PROPERTIES OF PARALLELOGRAMS
Example 2:
W
WXYZ is a parallelogram.
Find a and b.
6a  10
X
(18b  11)
Z
(9b  2)
8a  4
Y
6.2 PROPERTIES OF PARALLELOGRAMS
F
Example 3:
EFGH is a parallelogram.
Find w and z.
G
J
E
H
6.2 PROPERTIES OF PARALLELOGRAMS
Example 3:
Three vertices of JKLM are J(3,-8), K(-2,2) and
L(2,6). Find the coordinates of vertex M.
Step 1: Graph the given points
Step 2: Find the slope of KL .
Up 4, to the right 4
Step 3: Start at J and count Up
4, to the right 4
Step
4: Plot M and draw sides.
.
L
K
M
J