Proving Quadrilaterals

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• diagonals are mutual bisectors (6.3)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• diagonals are mutual bisectors (6.3)

• Not a parallelogram.

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

Which theorem can be used to prove the quadrilateral is a parallelogram?

• Parallelogram Opposite Sides Converse Theorem

• Parallelogram Opposite Angles Converse Theorem

• Opposite Sides Parallel and Congruent Theorem

• Parallelogram Diagonals Converse Theorem

Which method will NOT prove the quadrilateral is a parallelogram.

• Show that a pair of sides are congruent and parallel.

• Show that both pairs of opposite sides are congruent

• Show that both pairs of opposite sides are parallel

• Show that a pair of sides are parallel

Which theorem can be used to prove the quadrilateral is a parallelogram?

• Parallelogram Opposite Sides Converse Theorem

• Parallelogram Opposite Angles Converse Theorem

• Opposite Sides Parallel and Congruent Theorem

• Parallelogram Diagonals Converse Theorem

Which theorem can be used to prove the quadrilateral is a parallelogram?

• Parallelogram Opposite Sides Converse Theorem

• Parallelogram Opposite Angles Converse Theorem

• Opposite Sides Parallel and Congruent Theorem

• Parallelogram Diagonals Converse Theorem

Fill in the missing reason for the proof.

• Opposite angles are congruent.

• Alternate interior angles formed by parallel lines are congruent.

• Vertical angles are congruent.

• CPCTC

Is this enough information to prove this quadrilateral is a parallelogram?

• Yes, if two pairs of consecutive sides are congruent, then it is a parallelogram.

• No, there is not enough information.