Chapter 5Quadrilaterals5-1 Properties of Parallelograms

Definition of Parallelogram

A parallelogram (▱) is a quadrilateral with both pairs of opposite sides parallel.

Given: ▱EFGH

Prove: ;EF HG FG EH

E F

H G

Statements Reasons

1. EFGH is a parallelogram. 1. Given2. Draw auxiliary line 2. Through any two points

there is exactly one line.How would you finish the proof?

EG

Theorem 5-1: Opposite sides of a parallelogram are congruent.

1

23

4

Theorem 5-2

Opposite angles of a parallelogram are congruent.

M

S P

A

Theorem 5-3

Diagonals of a parallelogram bisect each other.

Properties of Parallelograms

The opposite sides are parallel (def)

The opposite sides are congruent (thm)

The opposite angles are congruent (thm)

The diagonals bisect each other (thm)