G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS
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Warm-Up/CFU
The measures of five of the interior angles of
a hexagon are 150°, 100°, 80°, 165°, and
150°. What is the measure of the sixth
interior angle?
1) 75° 2) 80° 3) 105° 4) 180°
Any polygon with four sides is a quadrilateral. However, some quadrilaterals have
special properties. These special quadrilaterals are given their own names.
A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a
parallelogram, you use the symbol
.
Given:
ABCD, identify all congruent ∡’s.
________
________
________
________
Hint: Look for pairs of alternate interior angles.
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS
Given:
2
ABCD, identify all congruent ∡’s.
________
________
________
________
________
________
________
________
Properties of Parallelograms
 If a quadrilateral is a parallelogram, then its opposite angles are congruent.

________
________
________
________
If a quadrilateral is a parallelogram, then its consecutive angles are
supplementary.
_______ + _______ = 180°
_______ + _______ = 180°
_______ + _______ = 180°
_______ + _______ = 180°
Example 1:
If the ∡
x = ______,
and
∡
∡
_______,
, solve for x and the following angle measures.
∡
_______,
∡
______,
∡
_____
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS
Example 2:
Given:
ABCD,
∡
and
∡
3
. Find the measure of all the
other angles.
m∡ACD = _______°
m∡B
= _______°
m∡BCA = _______°
m∡CAD = _______°

If a quadrilateral is a parallelogram, then its opposite sides are congruent.
________
________
________
________
Example 3: Solve for x and y.
AB = 4(x + 3); BC =
DC =
; AD = 3y
x = ______, y =_______
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS

4
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
A
B ________
________
________
________
E
C
D
Example 4: Solve for x and y.
BE =
, DE =
, AE =
, and AC =
.
x = ______, y =_______
B
A
E
D
C
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS
5
You Try It!
TX = 4y, YX = 30
XW = y + 3, XZ = 3y + 12
Solve for x and y.
x = ______, y =_______
x = ______, y =_______
NM ∥ KL, find x, m∡N, m∡K.
x = _______
m∡N = _______°
m∡K = _______°
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS
Challenge
In the accompanying diagram of parallelogram
ABCD, side AD is extended through D to E and DB
is a diagonal. If m∡EDC = 65° and m∡CBD = 85°,
find m∡CDB.
Exit Ticket
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
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G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS
Practice
Find the measurement indicated in each parallelogram.
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
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G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
8
G.CO.C.11 STUDENT NOTES-PROPERTIES OF PARALLELOGRAMS
HOMEWORK: Holt Textbook-Pg 395 #1-23, 33-43 ODD ALL work must be shown.
CHECK answers: pg 944
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