Question

1) Prove: A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and

congruent.​

Answer 1

Answer:

DEFINITION: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. THEOREM: If a quadrilateral has 2 sets of opposite sides congruent, then it is a parallelogram. THEOREM: If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Yes, this is true. If one pair of sides is both parallel and congruent, then you can prove the other pair of sides is also parallel (use SAS postulate to prove triangles are congruent).

Then by the definition of parallelogram this quadrilateral is a parallelogram.