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Introduction to Euclids Geometry MATHS - Introduction to Euclids Geometry

UP Board (UPMSP) - STD 9 - MATHS (UPMSP - English Medium). 48 questions in this chapter.

Question types

Introduction to Euclids Geometry question types

48 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

48
Questions
6
Question groups
5
Question types
Sample Questions

Introduction to Euclids Geometry questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 Mark
Write the correct answer in the following: It is known that if $x + y = 10$ then $x + y + z = 10 + z.$ The Euclid’s axiom that illustrates this statement is:
  • A
    First Axiom.
  • ✓
    Second Axiom.
  • C
    Third Axiom.
  • D
    Fourth Axiom.

Answer: B.

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Q 2M.C.Q1 Mark
Write the correct answer in the following: The number of dimensions, a surface has:
  • A
    $1$
  • ✓
    $2$
  • C
    $3$
  • D
    $0$

Answer: B.

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Q 3M.C.Q1 Mark
Write the correct answer in the following: Greek’s emphasised on:
  • A
    Inductive reasoning.
  • ✓
    Deductive reasoning.
  • C
    Both $A$ and $B$.
  • D
    Practical use of geometry.

Answer: B.

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Q 4M.C.Q1 Mark
Write the correct answer in the following: ‘Lines are parallel if they do not intersect’ is stated in the form of:
  • A
    An axiom.
  • ✓
    A definition.
  • C
    A postulate.
  • D
    A proof.

Answer: B.

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Q 5M.C.Q1 Mark
Write the correct answer in the following: The total number of propositions in the Elements are:
  • ✓
    $465$
  • B
    $460$
  • C
    $13$
  • D
    $55$

Answer: A.

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Q 8True False[1 Marks ]1 Mark
Write whether the following statements are True or False? Justify your answer: “For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l” is known as Playfair’s axiom.
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Q 9True False[1 Marks ]1 Mark
Write whether the following statements are True or False$?$ Justify your answer: If a quantity $B$ is a part of another quantity $A,$ then $A$ can be written as the sum of $B$ and some third quantity $C.$
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Q 112 Marks Questions2 Marks
Study the following statement: "Two intersecting lines cannot be perpendicular to the same line". Check whether it is an equivalent version to the Euclid’s fifth postulate. [Hint: Identify the two intersecting lines l and m and the linen in the above statement]
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Q 152 Marks Questions2 Marks
Read the following statements which are taken as axioms:
$i.$ If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
$ii.$ If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer.
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Q 183 Marks Question3 Marks
Read the following axioms:
$i.$ Things which are equal to the same thing are equal to one another.
$ii.$ If equals are added to equals, the wholes are equal.
$iii.$ Things which are double of the same thing are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.
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Q 193 Marks Question3 Marks
Solve the following question using appropriate Euclid’s axiom: Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.
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Q 215 Marks Questions5 Marks
In the:
$i. AB = BC, M$ is the mid$-$point of $AB$ and $N$ is the mid$-$ point of $BC.$ Show that $AM = NC.$
$ii. BM = BN, M$ is the mid$-$point of $AB$ and $N$ is the mid$-$point of $BC.$ Show that $AB = BC.$
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Q 224 Marks Questions4 Marks
Read the following statement: An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are $60^\circ $ each. Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.
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