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8.2 Properties of Parallelograms
Geometry
http://westm.schoolwires.net/Page/71
6
Objectives:
• Use some properties of parallelograms.
• Use properties of parallelograms in real-lie
situations
In this lesson . . .
And the rest of the chapter, you will study special
quadrilaterals. A parallelogram is a quadrilateral
with both pairs of opposite sides parallel.
If a quadrilateral is a
parallelogram, then
• Both pairs of opposite
sides are congruent
• Both pairs of opposite
angles are congruent
• Any pair of
consecutive angles are
supplementary, and
• The diagonals bisect
each other
P
180
Theorems about parallelograms
Q
R
• —If a quadrilateral
is a parallelogram,
then its opposite
sides are
congruent.
►PQ≅RS and
SP≅QR
P
S
Theorems about parallelograms
Q
R
• —If a quadrilateral
is a parallelogram,
then its opposite
angles are
congruent.
P ≅ R and
Q ≅ S
P
S
Theorems about parallelograms
Q
• —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°,
mR + mS = 180°,
mS + mP = 180°
P
R
S
Theorems about parallelograms
Q
R
• —If a quadrilateral
is a parallelogram,
then its diagonals
bisect each other.
QM ≅ SM and
PM ≅ RM
P
S
Ex. 1: Using properties of
Parallelograms
•
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: Using properties of parallelograms
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
PQRS is a parallelogram.
Find the value of x.
mS + mR = 180°
3x + 120 = 180
3x = 60
x = 20
S
3x°
120°
R
Consecutive s of a □ are supplementary.
Substitute 3x for mS and 120 for mR.
Subtract 120 from each side.
Divide each side by 3.
Q
http://www.khanacademy.org/math/geometry/quadrilaterals-andpolygons/v/proof---opposite-sides-of-parallelogram-congruent
http://www.khanacademy.org/math/geometry/quadrilaterals-andpolygons/v/proof---diagonals-of-a-parallelogram-bisect-each-other
http://www.khanacademy.org/math/geometry/quadrilaterals-andpolygons/v/proof---opposite-angles-of-parallelogram-congruent
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