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)

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. 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 any 2 methods.

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