Chapter 8.2 Notes: Use Properties of Parallelograms

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Chapter 8.2 Notes Use Properties of
Parallelograms

• Goal You will find angle and side measures in
  parallelograms.

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• A parallelogram is a quadrilateral with both
  pairs of opposite sides parallel.
• The term parallelogram PQRS can be written as
• Theorem 8.3
• If a quadrilateral is a parallelogram, then its
  opposite sides are congruent.
• If PQRS is a parallelogram, then ______________.

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• Theorem 8.4
• If a quadrilateral is a parallelogram, then its
  opposite angles are congruent.
• If PQRS is a parallelogram, then ______________.
• Ex.1 What is true about the two triangles formed
  by one diagonal of a parallelogram?

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• Ex.2 Find the values of x and y.
• Ex.3 Find the values of x and y.

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• Angles of a polygon that share a common side are
  consecutive angles.
• Theorem 8.5
• If a quadrilateral is a parallelogram, then its
  consecutive angles are supplementary.
• If PQRS is a parallelogram, then ______________.

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• Ex.4 In and
  Find
• the measures of
• B
  C
• 5
  3 4
• 
  
• 1 2
  6
• A
  D

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• Theorem 8.6
• If a quadrilateral is a parallelogram, then its
  diagonals bisect each other.
• Ex.5 Given Find the value of the
  variables.

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• Ex.6 Find the indicated measure in
• a. NM b. KM
• c. d.

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• Ex.7 Given
• Prove
• 
  G T
• E
  
• 
  N H
• L S