Transcript 6-2 Properties of Parallelograms

6-2 Properties of
Parallelograms
Ex. 1 Using Consecutive Angles
 In a parallelogram, consecutive angles are supplementary
 In a parallelogram, opposite angles are congruent
 What is ∠N?
112
 What is ∠T?
 180 – 112 = 68
 What is ∠S?
 68
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Ex. 2 Using Algebra
 Find x and then find QR and PS
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3𝑥 − 15 = 2𝑥 + 3
−2𝑥
− 2𝑥
𝑥 − 15 = 3
+15 + 15
𝑥 = 18
Plug in x to find QR or PS
 QR = 3 18 − 15
 QR = 54 − 15
 QR = 39
QR and PS are congruent
 PS = 39
Your Practice
 Find y and all the angles
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6𝑦 + 4 = 3𝑦 + 37
−3𝑦
− 3𝑦
3𝑦 + 4 = 37
−4 − 4
3𝑦 = 33
3𝑦
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3
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33
3
 𝑦 = 11
 ∠𝐹 = 110, ∠𝐺 = 70, ∠𝐻 = 110, ∠𝐸 = 70
Ex. 3 Using Algebra
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The diagonals of a parallelogram bisect each other
Solve systems of equations
Solve one set for one variable
B
Plug solved variable into other
equation
𝑦 =𝑥+1
2𝑥 = 3𝑦 − 7
2𝑥 = 3 𝑥 + 1 − 7
2𝑥 = 3𝑥 + 3 − 7
2𝑥 = 3𝑥 − 4
A
−2𝑥 − 2𝑥
0=𝑥 −4
+4
+4
4=𝑥
Plug solved letter into other equation to find missing variable
𝑦 = 4+1
𝑦=5
Then Plug in to find diagonal length
C
E
D
Your Practice
 Solve for a and b
X
 𝑎 =𝑏+2
Y
 2𝑎 − 8 = 𝑏 + 10
 2 𝑏 + 2 = 𝑏 + 10
 2𝑏 + 4 = 𝑏 + 10
 −𝑏
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−𝑏
𝑏 + 4 = 10
−4 − 4
𝑏=6
𝑎 = 6+2
𝑎=8
W
Z
Ex. 4 Parallel Lines
 If three or more parallel lines cuts one transversal
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into congruent segments, then they cut any
transversal into congruent segments.
EF ≅ FG ≅ GH
Find EH
EF + FG + HG = EH
2.5 + 2.5 + 2.5 = EH
EH = 7.5
Your Practice
 Find XV, TU, TZ
 XV = 2.25
 TU = 9
 TZ = 6