Parallelograms and Proving Parallelograms

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.

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.)

• 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

Match the missing statements & reasons in the proof.

f

b

d

e

a

c

g

ABCD Rhombus

Rhombus 4 = sides

Reflexive

Opp sides Parallel in Parallelogram

CPCTC

ABCD is Parallelogram

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.

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

Fill in the Reason.

• Opposite sides of a parallelogram are congruent.

• definition of parallelogram

• Prove

• CPCTC