6 3 Proving Quadrilaterals are Parallelograms Day 3

6. 3 Proving Quadrilaterals are Parallelograms Day 3

Warmup ã Find the slope of AB. Ý A(2, 1), B(6, 9) m=2 Ý A(-4, 2), B(2, -1) m= - ½ Ý A(-8, -4), B(-1, -3) m= 1/7

Review

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

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

ã 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.

ã 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.

Proving quadrilaterals are parallelograms Show that both pairs of opposite sides are parallel. ã Show that both pairs of opposite sides are congruent. ã Show that both pairs of opposite angles are congruent. ã Show that one angle is supplementary to both consecutive angles. ã

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

ã 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.

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