Proving a Quadrilateral Is a Parallelogram

Which statement about parallelograms is always true?

• The diagonals are congruent.

• The diagonals bisect each other.

• The diagonals are perpendicular.

• The diagonals bisect their respective angles.

If a quadrilateral has opposite sides that are congruent, what can you conclude about the shape?

• It is a kite

• It is a trapezoid

• It is a parallelogram

• Not enough information

If a quadrilateral has opposite angles that are congruent, what can you conclude about the shape?

• It is a trapezoid

• Not enough information

• It is a kite

• It is a parallelogram

Which additional fact would prove that quadrilateral WXYZ is a parallelogram?

For what value of x is JKLM a parallelogram?

• 7

• 14

• 21

• 28

For what values of a and b is the quadrilateral a parallelogram? a =​ (a)   and b =​ (b)  

• 64

• 10

• 17

• 128

• 32

• 12

• 5

• 20

For what values of a and b is the quadrilateral a parallelogram? a =​ (a)   and b =​ (b)  

• 4

• 17

• 8

• 3

• 12

• 15

• 2

• 5

If the diagonals of a quadrilateral bisect each other, what can you conclude about the shape? Choose all that apply.

• Parallelogram

• Kite

• Trapezoid

• Nothing can be concluded

The diagonals of quadrilateral ABCD intersect at point K. Is each of the following needed to prove that ABCD is a parallelogram?

Groups:

(a) Yes

,

(b) No

n quadrilateral PQRS, m∠RQS = 25 and PS = QR. What measure of ∠PSQ would confirm that PQRS is a parallelogram?

Mathematical Equivalence

ON