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Class 9 Maths — Euclid's geometry

Tell an axiom from a postulate, and use Euclid's first assumptions to justify a step.

Name: ________________________

Before you start

Four drawings, and the only difference between them is where they stop. Find out what each one is called.

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  1. 1. A point — no length at all
  2. 2. A line segment — an end at each side
  3. 3. A ray — one end, and no end the other way
  4. 4. A straight line — no ends at all

A point has no length, a segment has two ends, a ray has one and a line has none. Euclid's opening definitions are this list and very little else — everything afterwards is built out of these four.

  1. 1.How many straight lines can be drawn through two distinct points?

    • a) Exactly one
    • b) Infinitely many
    • c) None
    • d) Exactly two

  2. 2.In Euclid's system, what is a postulate?

    • a) An assumption made about geometry in particular
    • b) A word being given a meaning
    • c) A statement proved from earlier ones
    • d) A measurement taken off a drawing

  3. 3.If a = b and b = c, which of Euclid's axioms lets you write a = c?

    • a) Things which coincide with one another are equal
    • b) Things which are equal to the same thing are equal to one another
    • c) If equals are added to equals, the wholes are equal
    • d) The whole is greater than the part

  4. 4.If equals are subtracted from equals, the remainders are equal. Taking 8 from both sides of y + 8 = 15 gives what value of y?

  5. 5.Euclid's axiom says the whole is greater than the part. A segment 12 units long is cut into two parts and one of them is 5 units. How long is the other, in units?

  6. 6.How many straight lines can be drawn through a single point?

    • a) Exactly one
    • b) None
    • c) Infinitely many
    • d) Exactly two

  7. 7.Match each of Euclid's statements to what he called it.

    • A point is that which has no part
    • A straight line may be drawn from any point to any other point
    • The whole is greater than the part
    • The angles of a triangle add up to 180°
    • Postulate
    • Definition
    • Axiom
    • Theorem

  8. 8."Two distinct straight lines cannot have more than one point in common." In Euclid's scheme this is...

    • a) one of the axioms
    • b) a definition
    • c) a theorem, proved from the postulates
    • d) one of the five postulates

Answer key — Class 9 Maths — Euclid's geometry

  1. 1. a) Exactly one
  2. 2. a) An assumption made about geometry in particular
  3. 3. b) Things which are equal to the same thing are equal to one another
  4. 4. 7
  5. 5. 7
  6. 6. c) Infinitely many
  7. 7. A point is that which has no part → Definition; A straight line may be drawn from any point to any other point → Postulate; The whole is greater than the part → Axiom; The angles of a triangle add up to 180° → Theorem
  8. 8. c) a theorem, proved from the postulates