Question

If each pair of opposite sides of a quadrilateral are equal, then it is a :

• A. Square
• B. Parallelogram
• C. Rhombus
• D. Kite

Answer 1

The correct option is B Parallelogram


A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel.
Let $ABCD$ be a quadrilateral in which $AB=CD$ and $AB||CD$
Join A, C
Now, in Δ’s $ABCandADC$,
$AB=CD$ (Given)
$AC=AC$ (Common side)
$\angle BAC=\angle ACD$ (Alternate angles)
$\Delta ABC\cong \Delta CDA$ [By SAS Congruence criterion]
$\angle BCA=\angle DAC$ [CPCT]
Hence $AD||BC$ [Since alternate angles are equal, lines are parallel]
Thus in quadrilateral $ABCD,AB||CDandAD||BC$
Since both the pairs of opposite sides of quadrilateral are parallel, $ABCD$ is a parallelogram.