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6.3 Proving Quadrilaterals are Parallelograms

Learn how to prove quadrilaterals are parallelograms using different methods, such as comparing slopes and distances, and exploring properties like parallel sides, congruent sides, congruent angles, and bisecting diagonals. See examples with given vertex coordinates to practice the concepts.

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6.3 Proving Quadrilaterals are Parallelograms

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  1. 6.3 Proving Quadrilaterals are Parallelograms Day 3

  2. Warmup • Find the slope of AB. • A(2,1), B(6,9) m=2 • 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. Let’s 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.

  6. 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.

  8. 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.

  9. .. 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.

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

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