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

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EXERCISE 5.1 1–10 (part 1 of 5)

  1. Exercise 1

    The three steps from solids to points are : (A) Solids - surfaces - lines - points (B) Solids - lines - surfaces - points (C) Lines - points - surfaces - solids (D) Lines - surfaces - points - solids

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    (A)
    (A) Solids \(\displaystyle \rightarrow\) surfaces \(\displaystyle \rightarrow\) lines \(\displaystyle \rightarrow\) points.Each step drops one dimension: a solid's boundary is a surface, a surface's boundary is a line, and a line's boundary is a point.

  2. Exercise 2

    The number of dimensions, a solid has : (A) 1\displaystyle 1 (B) 2\displaystyle 2 (C) 3\displaystyle 3 (D) 0\displaystyle 0

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    (C)
    (C) \(\displaystyle 3\)A solid has length, breadth and height, three independent measures, so three dimensions.

  3. Exercise 3

    The number of dimensions, a surface has : (A) 1\displaystyle 1 (B) 2\displaystyle 2 (C) 3\displaystyle 3 (D) 0\displaystyle 0

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    (B)
    (B) \(\displaystyle 2\)A surface has length and breadth only, with no thickness, so it is two-dimensional.

  4. Exercise 4

    The number of dimension, a point has : (A) 0\displaystyle 0 (B) 1\displaystyle 1 (C) 2\displaystyle 2 (D) 3\displaystyle 3

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    (A)
    (A) \(\displaystyle 0\)A point has no length, breadth or height, no part at all, so it has zero dimensions.

  5. Exercise 5

    Euclid divided his famous treatise "The Elements" into : (A) 13\displaystyle 13 chapters (B) 12\displaystyle 12 chapters (C) 11\displaystyle 11 chapters (D) 9\displaystyle 9 chapters

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    (A)
    (A) $\displaystyle 13$ chaptersEuclid gathered the geometry and number theory known in his time into The Elements, organised as $\displaystyle 13$ books.

  6. Exercise 6

    The total number of propositions in the Elements are : (A) 465\displaystyle 465 (B) 460\displaystyle 460 (C) 13\displaystyle 13 (D) 55\displaystyle 55

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    (A)
    (A) \(\displaystyle 465\)Across its $\displaystyle 13$ books, The Elements states and proves $\displaystyle 465$ propositions, built from definitions, postulates and common notions.

  7. Exercise 7

    Boundaries of solids are : (A) surfaces (B) curves (C) lines (D) points

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    (A)
    (A) surfacesA solid occupies space; where it stops is a two-dimensional surface, its boundary.

  8. Exercise 8

    Boundaries of surfaces are : (A) surfaces (B) curves (C) lines (D) points

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    (B)
    (B) curves — A surface's edge need not be straight: a flat disc is bounded by a circle. A straight line is only a special case of a curve.

  9. Exercise 9

    In Indus Valley Civilisation (about 3000\displaystyle 3000 B.C.), the bricks used for construction work were having dimensions in the ratio (A) 1\displaystyle 1 : 3\displaystyle 3 : 4\displaystyle 4 (B) 4\displaystyle 4 : 2\displaystyle 2 : 1\displaystyle 1 (C) 4\displaystyle 4 : 4\displaystyle 4 : 1\displaystyle 1 (D) 4\displaystyle 4 : 3\displaystyle 3 : 2\displaystyle 2

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    (B)
    (B) \(\displaystyle 4:2:1\)Excavated Indus Valley bricks, about $\displaystyle 3000$ B.C., were made to this length-breadth-height ratio, among the earliest evidence of standardised measurement.

  10. Exercise 10

    A pyramid is a solid figure, the base of which is (A) only a triangle (B) only a square (C) only a rectangle (D) any polygon

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    (D)
    (D) any polygonA pyramid's base can be a triangle, square, pentagon or any polygon; the base's shape only names the pyramid, it does not restrict it.