If one pair of sides is both congruent and parallel, then the quadrilateral is a parallelogram.

Question

Using the the properties of parallelograms can you prove the quadrilateral is a parallelogram based on the given information?

(3 points)
Yes No

Answer 1

Yes, the quadrilateral can be proven to be a parallelogram based on the given information.

Proof:

To prove that a quadrilateral is a parallelogram, we can utilize the properties of parallel and congruent sides.

1. Given: One pair of opposite sides of the quadrilateral is both congruent and parallel.

2. Properties of Quadrilaterals: Recall that in a parallelogram, opposite sides are both parallel and congruent.

3. Applying the properties: Since we have one pair of sides that is parallel and congruent, we can apply the following reasoning:

   • Let the quadrilateral be ABCD.
   • Assume AB is congruent to CD (AB ≅ CD) and AB is parallel to CD (AB || CD).

4. Conclusion from the properties: According to the properties of parallelograms, if one pair of opposite sides of a quadrilateral is both congruent and parallel, then it meets the definition of a parallelogram.

Thus, we conclude that the quadrilateral ABCD is indeed a parallelogram.

Final Answer:

Yes