Let ABCD be a quadrilateral which satisfies any of the following conditions.
( i ) opposite sides are equal
( ii ) each diagonal of ABCD divides it into congruent triangles
( iii ) each pair of opposite angles are equal
( iv ) diagonals of ABCD bisect each other
Then ABCD has to be a _____________

Correct option is C

Solution:
(i) Opposite sides are equal:
If AB = CD and BC = AD, then by joining diagonal AC, triangles ABC and CDA are congruent (SSS). Hence, corresponding angles are equal, which implies opposite sides are parallel. Therefore, ABCD is a parallelogram.

(ii) Each diagonal divides it into congruent triangles:
If a diagonal divides the quadrilateral into two congruent triangles, then corresponding sides are equal. This reduces to condition (i), so ABCD is a parallelogram.

(iii) Each pair of opposite angles are equal:
If ∠A = ∠C and ∠B = ∠D, then using the angle sum property (360°), we get consecutive angles supplementary. Thus, opposite sides are parallel, and ABCD is a parallelogram.

(iv) Diagonals bisect each other:
If diagonals intersect at a point and bisect each other, then triangles formed are congruent. This gives parallel opposite sides. Hence, ABCD is a parallelogram.

Conclusion: Any one of the given conditions ensures that ABCD is a parallelogram.