1. Proving Quadrilaterals Are Parallelograms
Chapter 6 Section 6.3
Proving Quadrilaterals Are Parallelograms

2. If a quadrilateral is a parallelogram, then …
Quick Review
Some Properties of Parallelograms
Definition: A parallelogram is a quadrilateral with both pairs of opposite sides congruent
If a quadrilateral is a parallelogram, then …
Theorem 6.2
Theorem 6.3
Theorem 6.4
Theorem 6.5
both pairs of opposite sides are congruent
both pairs of opposite angles are congruent
consecutive angles are supplementary
diagonals bisect each other

3. Quadrilateral PQRS with both pairs of opposite sides congruent
Proving a Quad is a Parallelogram
Theorem
Theorem 6.6
If both pairs of opposite sides of a quadrilateral
are congruent, then the quadrilateral is a parallelogram
Quadrilateral PQRS with both pairs of opposite sides congruent
PQRS is a parallelogram

4. Quadrilateral PQRS with both pairs of opposite angles congruent
Proving a Quad is a Parallelogram
Theorem
Theorem 6.7
If both pairs of opposite angles of a quadrilateral
are congruent, then the quadrilateral is a parallelogram
Quadrilateral PQRS with both pairs of opposite angles congruent
PQRS is a parallelogram

5. PQRS is a parallelogram
Proving a Quad is a Parallelogram
Theorem
Theorem 6.8
If an angle of a quadrilateral is supplementary to both
of its consecutive angles, then the quadrilateral is
a parallelogram
mS + mP = 180 and mS + mR = 180
PQRS is a parallelogram

6. PQRS is a parallelogram
Proving a Quad is a Parallelogram
Theorem
Theorem 6.9
If the diagonals of a quadrilateral bisect each other,
then the quadrilateral is a parallelogram
and
PQRS is a parallelogram

7. PQRS is a parallelogram
Proving a Quad is a Parallelogram
Theorem
Theorem 6.10
If one pair of opposite sides of a quadrilateral are congruent
and parallel, then the quadrilateral is a parallelogram
and
PQRS is a parallelogram

8. Proving a Quad is a Parallelogram

9. Proving a Quad is a Parallelogram

10. Proving a Quad is a Parallelogram

11. Definition: Theorem 6.10: Theorem 6.6: Theorem 6.10: Definition:
Proving a Quad is a Parallelogram
Definition:
Theorem 6.10:
Theorem 6.6:
Theorem 6.10:
Definition:
Theorem 6.10:

12. Proving a Quad is a Parallelogram
Theorem 6.9:
Theorem 6.8:

13. Proving a Quad is a Parallelogram
For a Quadrilateral to be a parallelogram opposite sides must be congruent

14. Proving a Quad is a Parallelogram
For a Quadrilateral to be a parallelogram opposite angles must be congruent

15. Proving a Quad is a Parallelogram
For a Quadrilateral to be a parallelogram diagonals must bisect each other

16. Proving a Quad is a Parallelogram
2. Def.  ’s

17. Proving a Quad is a Parallelogram
2. Def.  ’s