Lines a, b, c and d all pass through the point P, which is not on line l. Which of them is parallel to l, and how many lines through P can be parallel to l?

Class 9Introduction to Euclid's GeometryGeometry — Foundations

Ab and d; there are two such lines
BOnly c; infinitely many such lines exist
COnly c; exactly one such line exists
DNone; every line through P meets l somewhere

Step-by-Step Solution

a, b and d cross l (their meeting points are marked); c runs at a constant distance from l and never meets it. Playfair's axiom: through a point not on a line there is exactly one line parallel to it.

Answer: C) Only c; exactly one such line exists

Key idea: The five postulates of Euclid

**Postulate 1**: A straight line may be drawn from any one point to any other point.

**Postulate 2**: A terminated line (segment) can be produced indefinitely (extended).

**Postulate 3**: A circle can be drawn with any centre and any radius.

**Postulate 4**: All right angles are equal to one another.

**Postulate 5** (the famous one): If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles (180°), then the two lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

These 5 statements are the seeds. Everything else in classical geometry grows from them.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Introduction to Euclid's Geometry practice questions

More Class 9 Introduction to Euclid's Geometry practice

Four straight roads in Chandigarh are shown; no two are parallel and no three pass…Using Euclid's construction, circles with centres A and B and radius AB = 5 cm are…Euclid wrote that the boundaries of a solid are surfaces, the ends of surfaces are lines…Which one of these is an AXIOM (common notion)?Which statement is a POSTULATE (geometry-specific)?