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Proving Quadrilaterals are Parallelograms

Learn how to prove that a quadrilateral is a parallelogram using methods such as slope, distance, congruent sides and angles, and diagonal bisectors. Practice with examples and take the learning quiz.

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Proving Quadrilaterals are Parallelograms

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  1. 6.3 Proving Quadrilaterals are Parallelograms Learning Target I can use prove that a quadrilateral is a parallelogram.

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

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

  9. 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.

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

  11. Pair-share on Proving Parallelogram • 1. Show that the quadrilateral with vertices A(-1, -2), B(5,3), C(6,6), and D(0,7) is a parallelogram using any methods. • 2. Show that A(2,-1), B(1,3), C(6,5), and D(7,1) are the vertices of a parallelogram. • 3. Show that A(3,5), B(9,7), C(10,4), and D(0,1) are the vertices of a parallelogram. • 4. Show that A(2,5), B(8,8), C(7,5), and D(1,2) are the vertices of a parallelogram.

  12. Learning Quiz • Show that A(1,7), B(6,9), C(8,4), and D(3,2) are the vertices of a parallelogram.

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