Q1.
Observe the following figures. Figs. (i), (ii), and (iii) are quadrilaterals, and the others are not. Why?
Answer
Because only (i), (ii) and (iii) are closed figures made of exactly four line segments, joined end to end, with no segment crossing another and no free ends.
Check each figure against the two conditions a quadrilateral must satisfy:
- it is closed — you can trace it and return to the starting point;
- it is made of four straight sides that meet only at their endpoints.
Figures (iv) and (v) fail one of these. One of them is not closed (a side is left open, so there is no fourth vertex to complete the figure), and the other has sides that cross each other, so the four segments do not enclose a single region.
Why it matters: the word quadrilateral comes from the Latin quadri (four) and latus (side). The definition is what lets us talk about “the four angles of the figure” at all — in (i), (ii) and (iii) each pair of sides that meet at a vertex makes exactly one interior angle, so the figure has four well-defined angles. A crossed or open figure has no such set of four angles.