source: ncert_exercises
topic: geometry
class_level: class_9
chapter: ch5
exercise: ex5.2
difficulty: intermediate
Class 9 | Ch5: Introduction to Euclid's Geometry | Exercise 5.2
Q1. How would you rewrite Euclid's fifth postulate so that it would be easier to understand? Answer: Euclid's 5th postulate (rewritten / Playfair's Axiom): "For every line l and every point P not lying on l, there exists a unique line m through P that is parallel to l." In other words: Through a point outside a line, exactly ONE parallel line can be drawn. ✅
Q2. Does Euclid's fifth postulate imply the existence of parallel lines? Explain. Answer: YES. If a line l falls on two lines m and n such that interior angles on one side sum to 180° (two right angles), then by Postulate 5, m and n will NOT meet on that side. The sum on the other side is also 180°, so they don't meet on that side either. Therefore m and n never meet → they are PARALLEL. ✅ Euclid's 5th postulate implies parallel lines exist.