A Study of all things 4 sided

Quadrilaterals Parallelograms

Definition: A quadrilateral with both pairs of opposite sides parallel.

Theorems 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.

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

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

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

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

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

Are 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

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

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

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

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

Definition: A quadrilateral with both pairs of opposite sides parallel. Both pair of opposite sides parallel  parallelogram

Area of a Parallelogram Area = base * height A = b * h h b

If you did things right, you should have only used 1 sheet of paper, right?