Question

The data marked in the squares , name the figure which is not a parallelogram.

Answer 1

Numbering starts from the leftmost figure.

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1) Opposite sides are equal $\implies$ quadrilateral is a parallelogram. (Can be proven using basic congruency theorems)

2)

Opposite sides are parallel $\implies$ trapezium.

But the other pair of sides are not parallel, hence in the general case this is not a parallelogram but is a trapezium with two equal sides.

3) One pair of opposite sides are congruent and parallel $\implies$ this is a parallelogram.

Proof: Join two vertices and you get that the two triangles formed are congruent.

4)

Diagonals are bisected at their intersections $\implies$ Quadrilateral is a parallelogram.

Show that the two opposite little triangles are congruent by using SAS test (or whatever you call it)

So the figure which is not a parallelogram is 2.