Question

Complete the following statement by means of one of those given in brackets against each:

If one pair of opposite sides are equal and parallel, then the figure is ........................

Options

• parallelogram

• rectangle

• trapezium

Answer 1

If one pair of opposite sides are equal and parallel, then the figure is parallelogram.

Reason:

In ΔABC and ΔCDA,

 AB = DC Given)

  AC = AC (Common)

 ∠BAC = ∠DCA (Because  AB || CD, Alternate interior angles are equal)

So, by SAS Congruence rule, we have

ΔABC ≅ ΔCDA

Also,

 ∠BCA =∠DAC (Corresponding parts of congruent triangles are equal)

But, these are alternate interior angles, which are equal.

 AD || BC

Thus,  AB || CD and AD || BC

Hence, quadrilateral ABCD is parallelogram