A Study of all things 4 sided

QUADRILATERALS

Quadrilaterals

Parallelograms

Parallelograms

Definition:A quadrilateral with both pairs of

opposite sides parallel.

Properties of ParallelogramsTheorems and Conclusions

Theorem # 28:If a quadrilateral is a

parallelogram, then the pairs of opposite sides are congruent. • Both pairs of

opposite sides

parallel

• Both pairs of

opposite sides

congruent.

Parallelograms

Theorem # 29:If a quadrilateral is a

parallelogram, then both pairs of opposite angles are congruent. • Both pairs of

opposite sides

parallel

• Both pairs of

opposite sides

congruent

• Both pairs of

opposite angles

congruent

Parallelograms

Theorem # 30:If a quadrilateral is a

parallelogram, then the pairs of consecutive angles are supplementary.

• Both pairs of

opposite sides

parallel

• Both pairs of

opposite sides

congruent

• Both pairs of

opposite angles

congruent

• Pairs of

consecutive angles

are supplementary

Parallelograms

1

2 3

41 2 180

2 3 180

3 4 180

4 1 180

Theorem # 31:If a quadrilateral is a

parallelogram, then the diagonals bisect each other. • Both pairs of

opposite sides

parallel

• Both pairs of

opposite sides

congruent

• Both pairs of

opposite angles

congruent

• Pairs of

consecutive angles

are supplementary

• Diagonals bisect

each other

Parallelograms

Example #1:Name any pairs of parallel sides.Name any pairs of congruent

segments.Name any pairs of congruent

angles.Name any pairs of supplementary

angles.

Answers:

A

B C

D

E

;AB CD BC AD

;AB CD BC AD

;AE EC BE ED

;ABC ADC

BCD DAB

180

180

180

180

A B

B C

C D

D A

Parallelogram “HOT FACTS”4 Sides –

Quadrilateral

2 pairs of opposite sides parallel

2 pairs of opposite sides congruent

2 pairs of opposite angles congruent

4 pairs of consecutive angles supplementary

Diagonals bisect each other

Proving Quadrilaterals are ParallelogramsAre you sure they’re parallelograms?

Theorem # 32:If a quadrilateral has both pairs of

opposite sides congruent, then the quadrilateral is a parallelogram. • BOTH pairs of

opposite sides

congruent

parallelogram

Parallelograms

Theorem # 33:If a quadrilateral has both pairs of

opposite angles congruent, then the quadrilateral is a parallelogram.

• BOTH pairs of

opposite sides

congruent

parallelogram

•BOTH pairs of

opposite angles

congruent

parallelogram

Parallelograms

Theorem # 34:If a quadrilateral has a pair of

consecutive angles supplementary, then the quadrilateral is a parallelogram.

• BOTH pairs of

opposite sides

congruent

parallelogram

•BOTH pairs of

opposite angles

congruent

parallelogram

• A pair of

consecutive

angles

supplementary

parallelogram

Parallelograms

1

2 3

41 2 180

2 3 180

3 4 180

4 1 180

Theorem # 35:If a quadrilateral’s diagonals

bisect each other, then the quadrilateral is a parallelogram. • BOTH pairs of

opposite sides

congruent

parallelogram

•BOTH pairs of

opposite angles

congruent

parallelogram

• A pair of

consecutive angles

supplementary

parallelogram

•Diagonals bisect

each other

parallelogram

Parallelograms

Theorem # 36:If a quadrilateral has exactly 1

pair of opposite sides congruent and parallel, then the quadrilateral is a parallelogram.

• BOTH pairs of

opposite sides

congruent

parallelogram

•BOTH pairs of

opposite angles

congruent

parallelogram

• A pair of

consecutive angles

supplementary

parallelogram

•Diagonals bisect

each other

parallelogram

•Exactly 1 pair of

opposite sides

congruent and

parallel

parallelogram

Parallelograms

Definition:A quadrilateral with both pairs of

opposite sides parallel.Both pair of

opposite sides

parallel

parallelogram

Parallelograms

Area of a Parallelogram

Area = base * heightA = b * h

h

b

Everything you ever wanted to know about Parallelograms…You now knowIf you did things right, you should have only used 1 sheet of paper, right?