Lesson 8.3: Show that a Quadrilateral is a Parallelogram

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Lesson 8.3 Show that a Quadrilateral is a
Parallelogram

• Geometry

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Theorem 8.7 Side Congruence Theorem

• If both pairs of opposite sides of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.
• Converse of Theorem 8.3

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Theorem 8.8Angle Congruence Theorem

• If both pairs of opposite angles of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.
• Converse of Theorem 8.4

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Theorem 8.9Congruent Parallel Theorem

• If one pair of opposite sides of a quadrilateral
  are congruent AND parallel, then the
  quadrilateral is a parallelogram.

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Theorem 8.10Diagonal Bisect Theorem

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

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Summary Ways to Prove a Quadrilateral is a
Parallelogram

• Show both pairs of opposite sides are parallel.
  Definition of Parallelogram
• Show both pairs of opposite sides are congruent.
  Side Congruence Th.
• Show both pairs of opposite angles are congruent.
  Angle Congruence Th.
• Show one pair of opposite sides are congruent and
  parallel. Congruent Parallel Th.
• Show the diagonals bisect each other. Diagonal
  Bisect Th.

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Examples
What theorem can you use to show that the
quadrilateral is a parallelogram?
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Check Your Progress
What theorem can you use to show that the
quadrilateral is a parallelogram?
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Warm-Up

• Find the slope of the line that passes through
  the points
• Find the midpoint of the segment that begins at
  and ends at .
• Find the distance between the points
  .

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Angle Congruence Th.
Side Congruence Th.
Congruent Parallel Th.
Diagonal Bisect Th.
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Board Points

• 30 point grade
• Each time you go to the board and complete a
  problem, explain you problem to the class and
  have the correct work and answer, you will
  receive 6 points.
• You need at least 5 visits to the board in order
  to receive the 30 points.
• Any additional boards points after 5 will be
  worth 3 extra credit points per problem.
• You will have until May 5th to go up 5 times
  (most likely one chance per week).

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Lesson 8.3 Show that a Quadrilateral is a
Parallelogram(part 2)

• Geometry

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Prove that a Quadrilateral is a Parallelogram on
a Coordinate Plane

• Given the ordered pairs of the vertices of a
  quadrilateral, you can prove whether the
  quadrilateral is a parallelogram or not.
• Some Concepts to remember
• Slope
• Distance Formula
• Midpoint Formula

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How to Prove a Quadrilateral is a Parallelogram
on a Coordinate Plan

• DEFINITION OF PARALLELOGRAM
• Find Slope of all 4 sides. Opposite sides need to
  have equal Slope.
• SIDE CONGRUENCE THEOREM
• Find distance of all 4 sides. Opposite sides need
  to be equal in distance.
• CONGRUENT PARALLEL THEOREM
• Find Slope of one pair of opposite sides. They
  need to be equal.
• Find distance of the same pair of opposite sides.
  They need to be equal.

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Homework

• WED 3/16
• Workbook Pg. 151
• 1-10 (all)
• Textbook Pg. 523
• 2-7 (all)
• THU 3/17
• Worksheet Packet
• 8.1 7-25 (odd)
• 8.2 5, 11-19 (odd)
• 8.3 1-13 (odd)