8'3 Tests for Parallelograms

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8.3 Tests for Parallelograms
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Quick Parallelogram Review!

• Definition
• Properties

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Tests for Parallelograms

• Theorem 8.9 -If both pairs of opposite sides are
  congruent the polygon is a
  parallelogram
• Theorem 8.10 -If both pairs of opposite angles
  are congruent the polygon is a
  parallelogram
• Theorem 8.11 -If diagonals bisect each other
• the polygon is a parallelogram

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Tests continued

• Theorem 8.12 -If 1 pair of opposite sides are
  congruent and parallel the
  polygon is a parallelogram

• Def -If opposite sides are parallel
  the polygon is a parallelogram

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Example (paragraph proof)
B
C

• Given ?ABD ?CDB.
• Prove ABCD is parallelogram

A
D
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Example or not???
2.
1.
38
84
16 cm
84
38
16 cm
3.
4.
20
14 m
9
14 m
9
15 m
15 m
20
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Example

• Find x and y so that its a parallelogram

4y
2y12
6x-12
x
2x36
5y
5x-28
6y-42
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Example

• Parallelogram or not? Use the method indicated.
• A(3,3), B(8,2), C(6,-1), D(1,0) slope formula

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Example

• Parallelogram or not? Use the method indicated.
• P(5,3), Q(1,-5), R(-6,-1), S(-2,-7) slope
  formula distance formula

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Assignment

• 8.3 worksheet