Parallelograms

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Lesson 5-1

• Parallelograms

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Definition

• The definition of a parallelogram
  A quadrilateral whose opposite sides are
  parallel.
• Its symbol is a small figure

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Naming a Parallelogram

• A parallelogram is named using all four vertices.
• You can start from any one vertex, but you must
  continue in a clockwise or counterclockwise
  direction.
• For example, this can be either
  ABCD or ADCB.

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Basic Properties

• There are four basic properties of all
  parallelograms.
• These properties have to do with the angles, the
  sides and the diagonals.

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Opposite Sides

• The opposite sides of every parallelogram are
  congruent.
• That means that .
• So, if AB 7, then _____ 7?

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Opposite Angles

• One pair of opposite angles are ltA and ltC. The
  other pair is ltB and ltD.
• The opposite angles in every parallelogram are
  congruent.
• Complete If mltA 75? and mltB 105 ?, then
  mltC ______ and mltD ______ .

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Consecutive Angles

• Each angle is consecutive to two other angles.
  ltA is consecutive with ltB and ltD.
• Each pair of consecutive angles is supplementary.
• Therefore, mltA mltB 180 and mltA mltD 180.
• If mltC 46 ?, then mltB _____?

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Diagonals

• Diagonals are segments that join non-consecutive
  vertices.
• For example, in this diagram, the only two
  diagonals are .

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Diagonal Property

• When the diagonals intersect, they meet at the
  midpoint of each diagonal.
• So, P is the midpoint of .
• Therefore, they bisect each other so
  and .
• But, the diagonals are not congruent!

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Parallelogram Summary

• By its definition, opposite sides are parallel.
• Other properties
• Opposite sides are congruent.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• The diagonals bisect each other.

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Examples

• 1. Draw HKLP.
• 2. Complete HK _______ and HP
  ________ .
• 3. mltK mlt______ .
• 4. mltL mlt______ 180?.
• 5. If mltP 65?, then mltH ____, mltK
  ______ and mltL ______ .

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Examples (contd)

• 6. Draw in the diagonals. They intersect at M.
• 7. Complete If HM 5, then ML ____ .
• 8. If KM 7, then KP ____ .
• 9. If HL 15, then ML ____ .
• 10. If mltHPK 36?, then mltPKL _____ .