Download 6-2 Parallelograms 12-17

12/18/2015
Five-Minute Check (over Lesson 6–1)
CCSS
Then/Now
New Vocabulary
Theorems: Properties of Parallelograms
Proof: Theorem 6.4
Example 1: Real-World Example: Use Properties of
Parallelograms
Theorems: Diagonals of Parallelograms
Example 2: Use Properties of Parallelograms and Algebra
Example 3: Parallelograms and Coordinate Geometry
Example 4: Proofs Using the Properties of Parallelograms
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Over Lesson 6–1
Find the measure of an interior angle of a regular
polygon that has 10 sides.
Find the measure of an interior angle of a regular
polygon that has 12 sides.
What is the sum of the measures of the interior
angles of a 20-gon?
What is the sum of the measures of the interior
angles of a 16-gon?
Find x if QRSTU is a regular
pentagon.
Over Lesson 6–1
Find the measure of an interior angle of a regular
polygon that has 10 sides.
A. 180
B. 162
C. 144
D. 126
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Over Lesson 6–1
Find the measure of an interior angle of a regular
polygon that has 12 sides.
A. 135
B. 150
C. 165
D. 180
Over Lesson 6–1
What is the sum of the measures of the interior
angles of a 20-gon?
A. 3600
B. 3420
C. 3240
D. 3060
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Over Lesson 6–1
What is the sum of the measures of the interior
angles of a 16-gon?
A. 3060
B. 2880
C. 2700
D. 2520
Over Lesson 6–1
Find x if QRSTU is a regular pentagon.
A. 21
B. 15.25
C. 12
D. 10
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Over Lesson 6–1
What type of regular polygon has interior angles
with a measure of 135°?
A. pentagon
B. hexagon
C. octagon
D. decagon
Content Standards
G.CO.11 Prove theorems about
parallelograms.
G.GPE.4 Use coordinates to prove simple
geometric theorems algebraically.
Mathematical Practices
4 Model with mathematics.
3 Construct viable arguments and critique the
reasoning of others.
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You classified polygons with four sides as
quadrilaterals.
• Recognize and apply properties of the sides
and angles of parallelograms.
• Recognize and apply properties of the
diagonals of parallelograms.
• parallelogram
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Use Properties of Parallelograms
A. CONSTRUCTION In
suppose
m∠
∠B = 32, CD = 80 inches, BC = 15 inches.
Find AD.
AD = BC
AD = 15
Answer: AD = 15 inches
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Use Properties of Parallelograms
B. CONSTRUCTION In
suppose
m∠
∠B = 32, CD = 80 inches, BC = 15 inches.
Find m∠
∠C
m∠C + m∠B = 180
m∠C + 32 = 180
m∠C = 148
Answer: m∠C = 148
Use Properties of Parallelograms
C. CONSTRUCTION In
suppose
m∠
∠B = 32, CD = 80 inches, BC = 15 inches.
Find m∠
∠D
m∠D = m∠B
m∠D = 32
Answer: m∠D = 32
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A. ABCD is a parallelogram. Find AB.
A. 10
B. 20
C. 30
D. 50
B. ABCD is a parallelogram. Find m∠
∠C.
A. 36
B. 54
C. 144
D. 154
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C. ABCD is a parallelogram. Find m∠
∠D.
A. 36
B. 54
C. 144
D. 154
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Use Properties of Parallelograms and Algebra
A. If WXYZ is a parallelogram, find the value of r.
Answer: r = 4.5
Use Properties of Parallelograms and Algebra
B. If WXYZ is a parallelogram, find the value of s.
8s = 7s + 3
s=3
Answer: s = 3
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Use Properties of Parallelograms and Algebra
C. If WXYZ is a parallelogram, find the value of t.
ܹܺ ∥ ܼܻ
∠YWX ≅ ∠WYZ
m∠YWX = m∠WYZ
2t = 18
t=9
A. If ABCD is a parallelogram, find the value of x.
A. 2
B. 3
C. 5
D. 7
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B. If ABCD is a parallelogram, find the value of p.
A. 4
B. 8
C. 10
D. 11
C. If ABCD is a parallelogram, find the value of k.
A. 4
B. 5
C. 6
D. 7
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Parallelograms and Coordinate Geometry
What are the coordinates of the intersection of the
diagonals of parallelogram MNPR, with vertices
M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)?
The diagonals of a parallelogram bisect each other so
the intersection point is the midpoint of either ‫ ܲܯ‬or ܴܰ.
Find the midpoint of ‫( ܲܯ‬or ܴܰ)
Midpoint Formula
What are the coordinates of the intersection of the
diagonals of parallelogram LMNO, with vertices
L(0, –3), M(–2, 1), N(1, 5), O(3, 1)?
A.
B.
C.
D.
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