Vidaara.orgClass 9 · Mathematics
CodeVID-M09-05-FIF-01
Euclid's Fifth Postulate — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The fifth postulate concerns:
- A.circles
- B.parallel lines
- C.right angles
- D.triangles
2.
Playfair's axiom gives how many parallels through an external point?
- A.zero
- B.exactly one
- C.two
- D.infinite
3.
The fifth postulate is also called the:
- A.circle postulate
- B.parallel postulate
- C.angle postulate
- D.line postulate
4.
Two lines parallel to the same line are:
- A.perpendicular
- B.parallel
- C.intersecting
- D.equal
5.
Changing the fifth postulate leads to:
- A.arithmetic
- B.non-Euclidean geometry
- C.algebra
- D.trigonometry
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
State Playfair's axiom.
7.
The fifth postulate is also known as the ___ postulate.
8.
Two lines parallel to the same line are:
9.
How many parallels to a given line pass through an external point (Euclidean)?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
State the Playfair (equivalent) version of Euclid's fifth postulate.
11.
If line $m\parallel l$ and $n\parallel l$, what can be said about $m$ and $n$?
12.
Why is the fifth postulate historically important?
13.
Does the fifth postulate hold on the surface of a sphere?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
State Euclid's fifth postulate and Playfair's version, and note their relationship.
15.
Prove that two distinct lines cannot have more than one point in common.
Answer Key
Section A — Multiple Choice Questions
- (B) parallel lines
- (B) exactly one
- (B) parallel postulate
- (B) parallel
- (B) non-Euclidean geometry
Section B — Short Answer (2 marks)
- Through a point not on a line, exactly one line parallel to it can be drawn.
- Parallel.
- Parallel to each other.
- Exactly one.
Section C — Short Answer (3 marks)
- Through a point not on a given line, exactly one line parallel to it can be drawn.
- $m\parallel n$.
- Attempts to prove it led to non-Euclidean geometries.
- No.
Section D — Long Answer (5 marks)
- Fifth: if a transversal makes interior angles on one side summing to less than two right angles, the lines meet on that side. Playfair: exactly one parallel through an external point. They are logically equivalent.
- If they shared two points they would coincide (a line through two points is unique) — so at most one common point.
Generated by Vidaara.org · Assignment VID-M09-05-FIF-01 · vidaara.org