7.3 Proving a Quadrilateral is a Parallelogram

Both pairs of opposite angles are congruent.

Both pairs of opposite sides are congruent.

Both pairs of diagonals bisect each other.

Both pairs of opposite sides are parallel.

Diagonals bisect each other

Diagonals are congruent

Both pairs of opposite sides are parallel

Both pairs of opposite angles are congruent

Yes, quadrilateral with 2 pairs of opposite sides ≅

Yes, quadrilateral with 2 pairs of opposite angles ≅

Yes, quadrilateral with diagonals bisecting each other

not a parallelogram

yes,opposite sides are congruent

no we can not prove it is a parallelogram

yes, one pair of sides are congruent and parallel

yes, opposite sides are parallel

yes, diagonals bisect each other

yes

no

x = 13

x = 15

x = 70

x = 10

yes

no

yes

no

both pairs of opposite angles are congruent

diagonals bisect each other

both pairs of opposite sides are congruent

consecutive angles are supplementary

yes

no

Both pairs of opposite angles are congruent.

Both pairs of opposite sides are congruent.

Both pairs of diagonals bisect each other.

Both pairs of opposite sides are parallel. 

x = 8

x = 26

x = 28

x = 38

7

3

35

27

5

35

75

55

Parallelogram Opposite Sides Converse Theorem

Parallelogram Opposite Angles Converse Theorem

Opposite Sides Parallel and Congruent Theorem

Parallelogram Diagonals Converse Theorem

y = 43

y = 26

x = 19

x = 10

Yes

No

Parallelogram Diagonals Converse

Parallelogram Opposite Sides Converse

Parallelogram Opposite Angles Converse

Opposite Sides Parallel and Congruent Theorem