GEOMETRY

PROVING A QUADRILATERAL IS A

PARALLELOGRAM Only one of the following needs to be shown:

1) Show that both pairs of opposite sides are parallel.

2) Both pairs of opposite sides are congruent.

3) Both pairs of opposite angles are congruent.

4) The diagonals bisect each other.

5) A pair of opposite sides is both parallel and congruent.

Example 1

Determine if the following quadrilaterals are parallelograms, if yes explain.

Example 2

Find x and y so that the quadrilateral is a parallelogram.

Example 3

Graph quadrilateral QRST with vertices Q(-1,3), R(3,1), S(2, -3), and T(-2,-1). Determine if it is a parallelogram using the slope formula.

Homework

Worksheet