Mathematics Class 9
Introduction to Euclid's Geometry: Axioms and Postulates
Learn Euclid's definitions, axioms and postulates, and build your first geometry proof.
11 lessons · ~78 min total
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Lessons in this topic
- 0 Start here A roadmap: why examples are not proof, what a definition may use, the axioms, the five postulates, and the parts of a proof. · 4 min You are here
- 1 Examples are not a reason A claim can pass forty tests and still be false. One counterexample ends it. · 7 min
- 2 What a definition may use A definition may use only words we already have. Point and line stay undefined. · 8 min
- 3 Two agreements all maths uses Two axioms: things equal to the same thing are equal, and equals added to equals stay equal. · 7 min
- 4 Postulates: the board's own rules Postulates are the axioms of the drawing board. They are about points, lines and circles. · 7 min
- 5 The five postulates Euclid started geometry from five postulates: three that draw, and two that make claims. · 8 min
- 6 A construction that never measures Each drawing step of the bisector construction is allowed by a postulate. No step measures. · 8 min
- 7 A square with the same ground A 9 by 4 courtyard and the square of side 6 that covers the same ground. · 8 min
- 8 What proofs are made of Undefined words, definitions, axioms, postulates, reasoning: the layers under every proof. · 7 min
- 9 The big picture Eight ideas in one table: the failed claim, definitions, axioms, postulates, construction, the square and proof. · 6 min
- 10 Track quiz A cheat-sheet table and eight questions, one for each idea. · 8 min
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