Tests for Parallelograms

SECTION 8.3

How can I tell if a quadrilateral is a parallelogram?How do I prove a set of points in the coordinate plane

form a parallelograms?

TESTING PARALLELOGRAMS

1. Are both pairs of opposite sides parallel?2. Are both pairs of opposite angles congruent?3. Are both pairs of opposite sides congruent?4. Do the diagonals bisect each other?5. Is one pair of opposite sides parallel and congruent?

TESTS FOR PARALLELOGRAMS

If you answer yes to one of these

questions, you have a parallelogram!

TESTING PARALLELOGRAMS

Which quadrilaterals are parallelograms? Justify your answer.

A B

CD

M N

OP

I J

KL

E F

GH

35

35

20 20

Find x so that the ABCD is a quadrilateral that is a parallelogram.

ALGEBRA

A B

CD

Find y so that the ABCD is a quadrilateral that is a parallelogram.

ALGEBRA

F

D E

G

To prove congruent sides:

Distance formula:

To prove parallel lines:

Slope formula:

COORDINATE PLANE

Determine if the quadrilateral is a parallelogram or not.

M(–3, 0), N(–1, 3), P(3, 2), and R(1, -1)? Use the slope formula.

EXAMPLE

EXAMPLES

Determine if the quadrilateral is a parallelogram or not.

M(–3, -1), N(–1, 3), P(3, 1), and R(1, -3)? Use the distance and slope formulas.

Page 421 14 – 32 (Evens)

HOMEWORK