Common Notions MCQs Quiz | Class 9

Class: IX | Subject: Mathematics (Code 041) | Unit: Unit IV: Geometry | Topic: Common Notions MCQs Quiz | Covering topics: Meaning; examples. Test your understanding of Euclids Common Notions and download the PDF answer key.

Overview: Euclid’s Common Notions

In Class 9 Mathematics, Unit IV (Geometry) introduces the foundations of Euclidean Geometry. Euclid organized his geometry into definitions, axioms (or common notions), and postulates. While postulates are assumptions specific to geometry, Common Notions (often called Axioms) are assumptions used throughout mathematics and not specifically linked to geometry alone.

The 7 Common Notions

According to the standard curriculum (NCERT), there are seven main common notions stated by Euclid:

  1. Things which are equal to the same thing are equal to one another.
    Example: If A = B and C = B, then A = C.
  2. If equals are added to equals, the wholes are equal.
    Example: If x = y, then x + z = y + z.
  3. If equals are subtracted from equals, the remainders are equal.
    Example: If x = y, then x – z = y – z.
  4. Things which coincide with one another are equal to one another.
    Example: If figure A fits exactly on figure B, they are identical in all respects.
  5. The whole is greater than the part.
    Example: If B is a part of A, then A > B.
  6. Things which are double of the same things are equal to one another.
    Example: If 2x = z and 2y = z, then x = y.
  7. Things which are halves of the same things are equal to one another.
    Example: If x/2 = z and y/2 = z, then x = y.

Key Applications

Concept Common Notion Used
Magnitudes Comparing lengths, areas, and volumes relies on the principle that the whole is greater than the part.
Algebraic Equations Solving linear equations often uses “equals added to equals” or “equals subtracted from equals”.
Geometric Proofs Superposition of figures (like proving triangles congruent) uses “things which coincide are equal”.

Quick Revision List

  • Axioms vs. Postulates: Axioms are general mathematical truths; Postulates are specific to geometry.
  • Universality: Common notions apply to arithmetic, algebra, and geometry alike.
  • Inequality: The 5th notion (Whole > Part) defines the concept of “greater than”.

Extra Practice Questions

  1. State the axiom used: If area(A) = area(B) and area(B) = area(C), then area(A) = area(C).
  2. Give a real-life example of “The whole is greater than the part”.
  3. If two circles coincide, what can you say about their radii?
  4. Solve x – 10 = 20 and state the common notion used in the first step.
  5. Does Euclid’s first axiom apply to volumes? (Yes/No)