Knowledge organisers

Introduction to Euclid's Geometry: Axioms and Postulates: CBSE Class 9 Maths knowledge organiser

Everything to know about introduction to euclid's geometry: axioms and postulates on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Axiom: A basic fact accepted without proof and used throughout mathematics.
Postulate: A basic assumption accepted without proof that is about geometry.
Theorem: A statement proved from axioms, postulates and earlier results.

Key formulas

Axioms: things equal to the same thing are equal; equals added to (or taken from) equals give equals; the whole is greater than the part
Postulates: a line through any two points; extend a segment; a circle with any centre and radius; all right angles equal
Postulate 5: interior angles on one side \(<180^\circ\) ⇒ lines meet on that side. Playfair: one parallel through a point not on a line
Measurement: \(C\) between \(A,B\) ⇒ \(AC+CB=AB\); a segment has exactly one mid-point

Worked example

\(A, B, C, D\) lie on a line in that order, with \(AB = CD\). Show that \(AC = BD\).

\(AC = AB + BC\) and \(BD = BC + CD\) (measurement). Since \(AB = CD\), adding \(BC\) to both gives \(AB + BC = CD + BC\) (Axiom 2), so \(AC = BD\).

Common mistakes

Mixing up axioms (for all of mathematics) and postulates (for geometry).
Quoting the axiom number without saying what it states: write the axiom in words.
Assuming a fact from the figure ("it looks equal") instead of giving a reason.
Reading Postulate 5 the wrong way round: the lines meet on the side where the two interior angles add to less than \(180^\circ\).

You should be able to…

Tell definitions, axioms, postulates and theorems apart and state Euclid's axioms and postulates in your own words.
Use the axioms to find lengths on a line and justify short steps, and apply the diagonal rule.
Justify a construction from the postulates and use Postulate 5 to decide where two lines meet.
Write a full argument from the axioms and prove that a mid-point is unique.

The printable sheet

Introduction to Euclid's Geometry: Axioms and Postulates knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Introduction to Euclid's Geometry: Axioms and Postulates knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Exploring Algebraic Identities · Linear Equations in Two Variables · Coordinate Geometry · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers