NCERT Solutions for Class 8th Maths Chapter 4 Introduction — In-text Questions
Book page 82 Updated on2026-09-19
Q1.
Observe the following figures. Figs. (i), (ii), and (iii) are quadrilaterals, and the others are not. Why?
The five figures (i) to (v) printed on page 82. In (i), (ii) and (iii) the angles between the sides are marked.
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 the second condition. Both are closed, but their boundaries are not made only of straight line segments: (iv) has three straight sides and one curved side, and (v) has two straight sides and two curved sides. A curve is not a side, so neither figure is built from four line segments.
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 figure whose boundary contains a curve has no such set of four angles.