Download Geometry Notes 6-2 Properties of Parallelograms Definition: A

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Geometry Notes
6-2 Properties of Parallelograms
Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
Properties
In a parallelogram:
1) Both pairs of opposite sides are congruent.
2) Both pairs of opposite angles are congruent.
3) Consecutive angles are supplementary.
4) Diagonals bisect each other.
Ex. 1: Correctly label each parallelogram and be familiar with them.
Add to 180°
Ex. 2: Using the parallelogram at the right, name the property that justifies each statement.
a) DE = EB
Diagonals bisect each other.
b) CB = AD
Opposite sides are congruent.
c) ∠DAB ≅ ∠BCD
Opposite angles are congruent.
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d)
Consecutive angles are supplementary.
e) 2AE = AC
Diagonals bisect each other.
Ex. 3: In the parallelogram at the right, find WX and
6a + 10 = 8a − 4
10 + 4 = 8a − 6a
14 = 2a
a=7
WX = 6(7) + 10 = 42 + 10 = 52
18b −11+ 9b + 2 = 180
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27b − 9 = 180
27b = 189
189
b=
=7
27
m∠Z = 9(7) + 2 = 63 + 2 = 65°
Ex. 4: In the parallelogram at the right,
a) Find m∠1.
3x + 25 = 5x − 5
€ 25 + 5 = 5x − 3x
30 = 2x
15 = x
m∠1 = 3(15) + 25 = 45 + 25 = 70°
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b) RB = x + 8, HB = 10x. Find HR.
2RB = HB
2( x + 8) = 10x
2x + 16 = 10x
16 = 8x
x =2
HR = RB = 2 + 8 = 10
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Ex. 5: In the parallelogram at the right, find x and y.
y=x+3
y + 7 = 3x
Substitute : x + 3 + 7 = 3x
x + 10 = 3x
10 = 2x
x =5
y =5+ 3=8
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y
y+7
3x
x+3
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