Questions & Answers: "Introduction To Euclidean Geometry"

Complete guide to "Introduction To Euclidean Geometry" for Math students. Below you will find important questions and model answers to help you prepare.

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Exemplar

28 Questions
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1.

Euclid’s second axiom (as per order given in the Textbook for Class IX) is

Options

❌

The things which are equal to the same thing are equal to one another.

✅

If equals be added to equals, the wholes are equal.

❌

If equals be subtracted from equals, the remainders are equals.

❌

Things which coincide with one another are equal to one another.

2.

Euclid’s fifth postulate is

Options

❌

The whole is greater than the part.

❌

A circle may be described with any centre and any radius.

❌

All right angles are equal to one another.

✅

If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

3.

The things which are double of the same thing are

Options

✅

equal

❌

unequal

❌

halves of the same thing

❌

double of the same thing

4.

Axioms are assumed

Options

✅

universal truths in all branches of mathematics.

❌

universal truths specific to geometry.

❌

theorems.

❌

definitions.

5.

John is of the same age as Mohan. Ram is also of the same age as Mohan. State the Euclid’s axiom that illustrates the relative ages of John and Ram

Options

✅

First Axiom

❌

Second Axiom

❌

Third Axiom

❌

Fourth Axiom

6.

: If a straight line falling on two straight lines makes the interior angles on the same side of it, whose sum is 120°, then the two straight lines, if produced indefinitely, meet on the side on which the sum of angles is

Options

❌

less than 120°

❌

greater than 120°

✅

is equal to 120°

❌

greater than 180°

7.

The three steps from solids to points are:

Options

✅

Solids - surfaces - lines - points

❌

Solids - lines - surfaces - points

❌

Lines - points - surfaces - solids

❌

Lines - surfaces - points - solids

8.

The number of dimensions, a solid has:

Options

❌

1

❌

2

✅

3

❌

0

9.

The number of dimensions, a surface has:

Options

❌

1

✅

2

❌

3

❌

0

10.

The number of dimensions, a point has:

Options

✅

0

❌

1

❌

2

❌

3

11.

Euclid divided his famous treatise “The Elements” into:

Options

✅

13 chapters

❌

12 chapters

❌

11 chapters

❌

9 chapters

12.

The total number of propositions in the Elements are:

Options

✅

465

❌

460

❌

13

❌

55

13.

Boundaries of solids are:

Options

✅

surfaces

❌

curves

❌

lines

❌

points

14.

Boundaries of surfaces are:

Options

❌

surfaces

✅

curves

❌

lines

❌

points

15.

In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio

Options

❌

1 : 3 : 4

✅

4 : 2 : 1

❌

4 : 4 : 1

❌

4 : 3 : 2

16.

A pyramid is a solid figure, the base of which is

Options

❌

only a triangle

❌

only a square

❌

only a rectangle

✅

any polygon

17.

The side faces of a pyramid are

Options

✅

Triangles

❌

Squares

❌

Polygons

❌

Trapeziums

18.

It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is:

Options

❌

First Axiom

✅

Second Axiom

❌

Third Axiom

❌

Fourth Axiom

19.

In ancient India, the shapes of altars used for household rituals were:

Options

✅

Squares and circles

❌

Triangles and rectangles

❌

Trapeziums and pyramids

❌

Rectangles and squares

20.

The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:

Options

❌

Seven

❌

Eight

✅

Nine

❌

Eleven

21.

Greeks emphasized on:

Options

❌

Inductive reasoning

✅

Deductive reasoning

❌

Both A and B

❌

Practical use of geometry

22.

In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for:

Options

✅

Public worship

❌

Household rituals

❌

Both Public worship and Household rituals

❌

None

23.

Euclid belongs to the country:

Options

❌

Babylonia

❌

Egypt

✅

Greece

❌

India

24.

Thales belongs to the country:

Options

❌

Babylonia

❌

Egypt

✅

Greece

❌

Rome

25.

Pythagoras was a student of:

Options

✅

Thales

❌

Euclid

❌

Both A and B

❌

Archimedes

26.

Which of the following needs a proof?

Options

✅

Theorem

❌

Axiom

❌

Definition

❌

Postulate

27.

Euclid stated that all right angles are equal to each other in the form of

Options

❌

an axiom

❌

a definition

✅

a postulate

❌

a proof

28.

‘Lines are parallel if they do not intersect’ is stated in the form of

Options

❌

an axiom

✅

a definition

❌

a postulate

❌

a proof