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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-05-AXM-01
Definitions, Axioms & Postulates — Assignment
Chapter: Euclid's Geometry
Topic: Definitions, Axioms and Postulates
Maximum Marks: 35
Time: 75 minutes
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.
"Things equal to the same thing are equal" is an:
  • A.axiom
  • B.postulate
  • C.theorem
  • D.definition
2.
"A line may be drawn from any point to any point" is a:
  • A.axiom
  • B.postulate
  • C.theorem
  • D.corollary
3.
An axiom is assumed:
  • A.false
  • B.true without proof
  • C.proved
  • D.approximately
4.
"The whole is ___ than the part."
  • A.less
  • B.greater
  • C.equal
  • D.double
5.
A statement that is proved is a:
  • A.postulate
  • B.theorem
  • C.axiom
  • D.definition
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $a=b$ and $b=c$, then $a=?$
7.
If equals are added to equals, the wholes are:
8.
Is "all right angles are equal" a postulate?
9.
Is a postulate proved or assumed?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
State Euclid's first postulate.
11.
State Euclid's third postulate.
12.
If $x+y=10$ and $x=4$, by which axiom is $y=6$?
13.
Give an example of a common notion (axiom).
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
State all five of Euclid's postulates briefly.
15.
If $AC=BD$, $AC=AB+BC$ and $BD=BC+CD$, prove that $AB=CD$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) axiom
  2. (B) postulate
  3. (B) true without proof
  4. (B) greater
  5. (B) theorem
Section B — Short Answer (2 marks)
  1. $c$.
  2. Equal.
  3. Yes (Euclid's fourth).
  4. Assumed.
Section C — Short Answer (3 marks)
  1. A straight line can be drawn from any one point to any other point.
  2. A circle can be drawn with any centre and any radius.
  3. If equals are subtracted from equals, the remainders are equal.
  4. The whole is greater than the part.
Section D — Long Answer (5 marks)
  1. (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.
  2. $AB=CD$ (subtracting the equal $BC$ from equals).
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