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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Euclid’s second axiom (as per order given in the Textbook for Class IX) is
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.
Euclid’s fifth postulate is
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.
The things which are double of the same thing are
equal
unequal
halves of the same thing
double of the same thing
Axioms are assumed
universal truths in all branches of mathematics.
universal truths specific to geometry.
theorems.
definitions.
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
First Axiom
Second Axiom
Third Axiom
Fourth Axiom
: 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
less than 120°
greater than 120°
is equal to 120°
greater than 180°
The three steps from solids to points are:
Solids - surfaces - lines - points
Solids - lines - surfaces - points
Lines - points - surfaces - solids
Lines - surfaces - points - solids
The number of dimensions, a solid has:
1
2
3
0
The number of dimensions, a surface has:
1
2
3
0
The number of dimensions, a point has:
0
1
2
3
Euclid divided his famous treatise “The Elements” into:
13 chapters
12 chapters
11 chapters
9 chapters
The total number of propositions in the Elements are:
465
460
13
55
Boundaries of solids are:
surfaces
curves
lines
points
Boundaries of surfaces are:
surfaces
curves
lines
points
In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio
1 : 3 : 4
4 : 2 : 1
4 : 4 : 1
4 : 3 : 2
A pyramid is a solid figure, the base of which is
only a triangle
only a square
only a rectangle
any polygon
The side faces of a pyramid are
Triangles
Squares
Polygons
Trapeziums
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is:
First Axiom
Second Axiom
Third Axiom
Fourth Axiom
In ancient India, the shapes of altars used for household rituals were:
Squares and circles
Triangles and rectangles
Trapeziums and pyramids
Rectangles and squares
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:
Seven
Eight
Nine
Eleven
Greeks emphasized on:
Inductive reasoning
Deductive reasoning
Both A and B
Practical use of geometry
In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for:
Public worship
Household rituals
Both Public worship and Household rituals
None
Euclid belongs to the country:
Babylonia
Egypt
Greece
India
Thales belongs to the country:
Babylonia
Egypt
Greece
Rome
Pythagoras was a student of:
Thales
Euclid
Both A and B
Archimedes
Which of the following needs a proof?
Theorem
Axiom
Definition
Postulate
Euclid stated that all right angles are equal to each other in the form of
an axiom
a definition
a postulate
a proof
‘Lines are parallel if they do not intersect’ is stated in the form of
an axiom
a definition
a postulate
a proof