6-4 Proving a Quadrilateral is a Parallelogram

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

What is the relationship between the diagonals of a parallelogram?

• They are parallel to each other

• They bisect each other

• They are equal in length

• They are perpendicular to each other

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

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

For what value of x is JKLM a parallelogram?

• 7

• 14

• 21

• 28

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

Given quadrilateral DEFG, if ∠EDG is​ (a)   to ∠ (b)   and ∠​ (c)   , then DEFG is a parallelogram. [Note: angle answers go in alphabetical order.]

• supplementary
• DEF
• DGF
• complementary
• congruent
• similar
• EFG
• GDE

Is there enough information to prove each quadrilateral is a parallelogram?

Groups:

(a) Yes

,

(b) No

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