chapter 5: quadrilaterals 5-2: ways to prove quadrilaterals are parallelgorams

CHAPTER 5:QUADRILATERALS

5-2:

WAYS TO PROVE QUADRILATERALS ARE

PARALLELGORAMS

PARALLELOGRAMS

• Remember that a parallelogram, by definition, is a quadrilateral with both pairs of opposite sides parallel.

• Conversely, if both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.

THEOREMS

Besides proving both pairs of opposite sides parallel, there are other ways to prove that quadrilaterals are parallelograms:

THEOREMS 5-4 through 5-7

Pg. 172 of the textbook

THEOREM 5-4

THEOREM 5-4:

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

PG. 173, CE 1

THEOREM 5-5THEOREM 5-5:

If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.

PG. 173, CE 8

THEOREM 5-6

THEOREM 5-6:

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

PG. 173, CE 6

THEOREM 5-7

THEOREM 5-7:

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

PG. 173, CE 4

ALWAYS, SOMETIMES, NEVER

1. If the measures of two angles of a quadrilateral are equal, then the quadrilateral is ________ a parallelogram.

2. If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is ________ a parallelogram.

3. To prove a quadrilateral is a parallelogram, it is ________ enough to show that one pair of opposite sides is parallel.

1. Sometimes

2. Always

3. Never

State the definition or theorem that enables you to deduce, from the given information, that quadrilateral ABCD is a parallelogram:

1. BE = ED; CE = EA

If the diagonals of a

quadrilateral bisect each other, then the quadrilateral is a parallelogram.

(Theorem 5-7)

B C

A D

E

CLASSWORK/HOMEWORK

• CW: Pg. 173, Classroom Exercises 1-9, 12-13

• HW: Pg. 174, Written Exercises 1-10