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NCERT Exemplar · Class 9 Mathematics Introduction to Euclid's Geometry

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EXERCISE 5.1 11–22 (part 2 of 5)

  1. Exercise 11

    The side faces of a pyramid are : (A) Triangles (B) Squares (C) Polygons (D) Trapeziums

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    (A)
    (A) TrianglesWhatever the base, each side face rises from one base edge to the single apex, so every lateral face is a triangle.

  2. Exercise 12

    It is known that if x+y=10\displaystyle x+y=10 then x+y+z=10+z\displaystyle x+y+z=10+z. The Euclid's axiom that illustrates this statement is : (A) First Axiom (B) Second Axiom (C) Third Axiom (D) Fourth Axiom

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    (B)
    (B) Second Axiom\[x+y=10 \] \[x+y+z = 10+z \quad \text{(adding \(\displaystyle z\) to both sides)} \]Euclid's second common notion: if equals are added to equals, the wholes are equal, exactly the step from the given equation to this one.

  3. Exercise 13

    In ancient India, the shapes of altars used for house hold rituals were : (A) Squares and circles (B) Triangles and rectangles (C) Trapeziums and pyramids (D) Rectangles and squares

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    (A)
    (A) Squares and circles — altars built for household rituals under the Sulbasutras were squares and circles; combinations of triangles, rectangles and trapeziums were reserved for public worship altars.

  4. Exercise 14

    The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is: (A) Seven (B) Eight (C) Nine (D) Eleven

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    (C)
    (C) Nine — the Sriyantra described in the Atharvaveda is formed of nine interwoven isosceles triangles, enclosed within a square and circle.

  5. Exercise 15

    Greek's emphasised on : (A) Inductive reasoning (B) Deductive reasoning (C) Both A and B (D) Practical use of geometry

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    (B)
    (B) Deductive reasoning — the Greeks built geometry on axioms and postulates, deriving every further result by logical deduction rather than by measurement or practical need.

  6. Exercise 16

    In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for : (A) Public worship (B) Household rituals (C) Both A and B (D) None of A, B, C

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    (A)
    (A) Public worship — altars combining rectangles, triangles and trapeziums were built for public worship, while household rituals used only squares and circles.

  7. Exercise 17

    Euclid belongs to the country: (A) Babylonia (B) Egypt (C) Greece (D) India

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    (C)
    (C) Greece — Euclid was a Greek mathematician; he taught at Alexandria in Egypt around $\displaystyle 300$ BCE, where he compiled the thirteen books of the Elements.

  8. Exercise 18

    Thales belongs to the country : (A) Babylonia (B) Egypt (C) Greece (D) Rome

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    (C)
    (C) Greece — Thales, from Miletus in Greece, was among the first to use deductive reasoning to establish geometric results rather than rely on observation.

  9. Exercise 19

    Pythagoras was a student of : (A) Thales (B) Euclid (C) Both A and B (D) Archimedes

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    (A)
    (A) Thales — Pythagoras studied under Thales before going on to found his own school of mathematics and philosophy at Croton.

  10. Exercise 20

    Which of the following needs a proof? (A) Theorem (B) Axiom (C) Definition (D) Postulate

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    (A)
    (A) Theorem — a theorem is a statement established through logical proof from earlier results; axioms, postulates and definitions are the assumptions accepted without proof.

  11. Exercise 21

    Euclid stated that all right angles are equal to each other in the form of (A) an axiom (B) a definition (C) a postulate (D) a proof

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    (C)
    (C) a postulate — Euclid lists it as his fourth postulate, an assumption specific to geometry that is accepted without proof, not a general axiom.

  12. Exercise 22

    'Lines are parallel if they do not intersect' is stated in the form of (A) an axiom (B) a definition (C) a postulate (D) a proof

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    (B)
    (B) a definition — Euclid's Definition $\displaystyle 23$ fixes parallel lines as coplanar lines that, produced indefinitely, never meet; it names what the term means, not an assumption.