Question

If a pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a:

• A. rectangle
• B. parallelogram
• C. square
• D. rhombus

Answer 1

The correct option is B parallelogram

Consider a quadrilateral ABCD in which AB = CD and AB || CD. Let's construct the diagonal AC.
In △ABC and △CDA,
AB = CD [Given]
∠CAB = ∠ACD [Alternate interior angles]
AC = CA [Common side]

Thus, by SAS congruence,
△ABC ≅ △CDA
Hence, BC = DA. [CPCT]

In quadrilateral ABCD,
AB = CD [Given]
BC = DA [Proved above]
Thus, both the pairs of opposite sides of the given quadrilateral ABCD are equal.
Hence, ABCD is a parallelogram.