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 THEOREMS 5-4 through 5-7 Pg. 172 of the textbook 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 5-5 THEOREM 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 If the measures of two angles of a quadrilateral are equal, then the quadrilateral is ________ a parallelogram. If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is ________ a parallelogram. To prove a quadrilateral is a parallelogram, it is ________ enough to show that one pair of opposite sides is parallel.

State the definition or theorem that enables you to deduce, from the given information, that quadrilateral ABCD is a parallelogram: BE = ED; CE = EA If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. (Theorem 5-7) B C E A D

CLASSWORK/HOMEWORK CW: Pg. 173, Classroom Exercises 1-9, 12-13 HW: Pg. 174, Written Exercises 1-10