6.3 Proving Quadrilaterals are Parallelograms

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6.3 Proving Quadrilaterals are Parallelograms

• Day 3

2
Warmup

• Find the slope of AB.
• A(2,1), B(6,9)
• m2
• A(-4,2), B(2, -1)
• m - ½
• A(-8, -4), B(-1, -3)
• m 1/7

3
Review
4
Using properties of parallelograms.

• Method 1
• Use the slope formula to show that opposite
  sides have the same slope, so they are parallel.
• Method 2
• Use the distance formula to show that the
  opposite sides have the same length.
• Method 3
• Use both slope and distance formula to show one
  pair of opposite side is congruent and parallel.

5
Lets apply

• Show that A(2,0), B(3,4), C(-2,6), and D(-3,2)
  are the vertices of parallelogram by using method
  1.

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• Show that the quadrilateral with vertices
  A(-3,0), B(-2,-4), C(-7, -6) and D(-8, -2) is a
  parallelogram using method 2.

7

• Show that the quadrilateral with vertices A(-1,
  -2), B(5,3), C(6,6), and D(0,7) is a
  parallelogram using method 3.

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Proving quadrilaterals are parallelograms

• Show that both pairs of opposite sides are
  parallel.
• Show that both pairs of opposite sides are
  congruent.
• Show that both pairs of opposite angles are
  congruent.
• Show that one angle is supplementary to both
  consecutive angles.

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.. continued..

• Show that the diagonals bisect each other
• Show that one pair of opposite sides are
  congruent and parallel.

10

• Show that the quadrilateral with vertices A(-1,
  -2), B(5,3), C(6,6), and D(0,7) is a
  parallelogram using method 3.

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• Show that A(2,-1), B(1,3), C(6,5), and D(7,1) are
  the vertices of a parallelogram.