Vidaara.orgClass 9 · Mathematics
CodeVID-M9-05-CT
Introduction to Euclid's Geometry — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- 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.
Euclid's treatise is called:
- A.Principia
- B.The Elements
- C.Almagest
- D.Sphere
2.
"Things equal to the same thing are equal" is an:
- A.axiom
- B.postulate
- C.theorem
- D.definition
3.
The fifth postulate concerns:
- A.circles
- B.parallel lines
- C.right angles
- D.triangles
4.
A point has:
- A.length
- B.no part
- C.area
- D.volume
5.
"A line may be drawn from any point to any point" is a:
- A.axiom
- B.postulate
- C.theorem
- D.corollary
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
How many dimensions does a point have?
7.
If $a=b$ and $b=c$, then $a=?$
8.
State Playfair's axiom.
9.
How many dimensions does a line have?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
State Euclid's definition of a point.
11.
State Euclid's first postulate.
12.
State the Playfair (equivalent) version of Euclid's fifth postulate.
13.
State Euclid's definition of a line.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Distinguish between an axiom and a postulate as used by Euclid, with one example of each.
15.
State all five of Euclid's postulates briefly.
Answer Key
Section A — Multiple Choice Questions
- (B) The Elements
- (A) axiom
- (B) parallel lines
- (B) no part
- (B) postulate
Section B — Short Answer (2 marks)
- $0$.
- $c$.
- Through a point not on a line, exactly one line parallel to it can be drawn.
- $1$.
Section C — Short Answer (3 marks)
- That which has no part.
- A straight line can be drawn from any one point to any other point.
- Through a point not on a given line, exactly one line parallel to it can be drawn.
- Breadthless length.
Section D — Long Answer (5 marks)
- Axiom = common notion (general truth, e.g. "things equal to the same thing are equal"); postulate = a geometric assumption (e.g. "a line can be drawn between any two points").
- (1) A line between two points; (2) a segment can be extended indefinitely; (3) a circle of any centre and radius; (4) all right angles are equal; (5) the parallel postulate.
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