1) A parallelogram is a quadrilateral with both pairs of opposite sides parallel. 2) The document proves that in a parallelogram, opposite sides are congruent and opposite angles are congruent. 3) It also states that the diagonals of a parallelogram bisect each other.

1. Chapter 5
Parallelograms
5-1 Properties of Parallelograms

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

3. Theorem 5-1: Opposite sides of a parallelogram are congruent.
H
G
Given: ▱EFGH
Prove: EF HG ; FG
4
1
EH
2
E
3
Statements
Reasons
1. EFGH is a parallelogram.
2. Draw auxiliary line EG
1. Given
2. Through any two points
there is exactly one line.
How would you finish the proof?
F

4. Theorem 5-2
 Opposite angles of a parallelogram are
congruent.
M
S
A
P

5. Theorem 5-3
Diagonals of a parallelogram
bisect each other.

6. 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)