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. MMethod 1 Use the slope formula to show that opposite sides have the same slope, so they are parallel. MMethod 2 Use the distance formula to show that the opposite sides have the same length. M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.  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. Pair-share on Proving 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.