Download 6.2 Properties of Parallelograms

Geometry
6.2
Parallelograms
-A parallelogram is a quadrilateral with both
pairs of opposite sides parallel.
-The symbol
PQRS is read “parallelogram
PQRS.”
Theorem 6.3
Q
R
• If a quadrilateral is a
parallelogram, then its
opposite sides are
congruent.
P
S
Theorem 6.4
Q
R
• If a quadrilateral is a
parallelogram, then its
opposite angles are
congruent.
P
S
Theorem 6.5
Q
R
• If a quadrilateral is a
parallelogram, then its
consecutive angles are
supplementary (add up
to 180°).
mP +mQ = 180°,
mQ +mR = 180°
P
S
Theorem 6.6
• -If one angle of a parallelogram is right,
then all 4 angles are right.
Theorem 6.7
Q
R
• If a quadrilateral is a
parallelogram, then its
diagonals bisect each
other.
P
S
Ex. 1
•
FGHJ is a
parallelogram. Find
the unknown length.
Explain your
reasoning.
a. JH
b. JK
5
F
G
K
J
b.
3
H
Ex. 2
Q
PQRS is a parallelogram.
Find the angle measure.
a. mR
b. mQ
P
R
70°
S
Ex. 3: Using Algebra with Parallelograms
P
Q
PQRS is a parallelogram.
Find the value of x.
S 3x°
120°
R
Ex. 4
Given: ABCD and
AEFG are
parallelograms.
Prove 1 ≅ 3.
A
E
B
2
D
1
C
G
3
F
Example 5
• What are the coordinates of the intersection
of the diagonals of parallelogram MNPR
with vertices M(-3,0), N(-1, 3), P(5, 4),
R(3,1)?
Homework
• Page 403: (2-21, 31-36, 50-57) all