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

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

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

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

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

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

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

Proving a Quad is a Parallelogram

Proving a Quad is a Parallelogram

Proving a Quad is a Parallelogram

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:

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

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

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

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

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

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