Section 6'3 Proving that a Quadrilateral is a Parallelogram

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Section 6.3Proving that a Quadrilateral is a
Parallelogram

• Remember how we learned Parallel lines and a
  transversal?
• Then we learned given two lines and a transversal
  we PROVED which lines were parallel
• Yesterday we leaned properties of a
  Parallelogram.
• Today we prove its a Parallelogram
• (Just like Chapter 3)

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Review First

• If a Quadrilateral is a Parallelogram, what did
  you learn yesterday? What properties do you know?

• Opposite Sides are Parallel
• Opposite Sides are Congruent
• Opposite Angles are Congruent
• Consecutive Angles are Supplementary
• Diagonals Bisect each other

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Theorem 6.5

• If the diagonals of a quadrilateral bisect each
  other, then the quadrilateral is a parallelogram.

C
B
E
A
D
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Theorem 6.6

• If one pair of opposite sides of a quarilateral
  is BOTH congruent and parallel, then the
  quadrilateral is a parallelogram.

Informal Proof Diagaonals and Triangles!
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Examples (p307)

• Find the value of the variables SO THAT the
  quadrilateral is a parallelogram.

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You Try page 307 s 4-6
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Theorem 6.7 6.8

• If both pairs of opposite sides angles of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.

G
Y
B
A
C
D
M
Mark what we need to know to say MAGY and ABCD
are Parallelograms by THM 6.7 6.8.
A
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Proof of Theorem 6.8 (p308)
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Do you have enough information to say the
following are parallelograms?
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Example page 308 26
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Example p 308 27
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Example p308 28 29
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Exercises

• Page 310 7 8
• Page 695 5 12
• WB page 68