Welcome to your quick revision of Class 9 Maths, Chapter 5 – Euclid’s Geometry! Here you’ll find MCQs that challenge your understanding and fill-in-the-blanks that test your memory of important points. Each question has an answer provided, so you can learn and correct yourself instantly. A simple, student-friendly way to get exam-ready!
Class 9th Maths Important MCQs with Answers from Chapter 5 – Introduction to Euclid’s Geometry
Question 1. The word ‘geometry’ comes from the Greek words ‘geo’ and ‘metrein’, which mean:
a) Earth and measure
b) Land and build
c) Space and divide
d) Line and angle
Answer:
a) Earth and measure – ‘Geo’ means earth and ‘metrein’ means to measure.
Question 2. Euclid is famous for his treatise on geometry known as:
a) The Republic
b) Elements
c) Calculus
d) Theorems of Geometry
Answer:
b) Elements – Euclid’s “Elements” is a collection of 13 books on geometry.
Question 3. A point, according to Euclid’s definition, is:
a) A dot with some thickness
b) That which has no part
c) A tiny circle
d) The intersection of two lines
Answer:
b) That which has no part – Euclid’s first definition of a point.
Question 4. According to Euclid, a line is defined as:
a) A collection of points
b) Breadthless length
c) Length with width
d) Infinite set of points
Answer:
b) Breadthless length – Euclid’s definition of a line.
Question 5. The ends of a line are called:
a) Rays
b) Dots
c) Points
d) Surfaces
Answer:
c) Points – Euclid’s definition 3 states that the ends of a line are points.
Question 6. Which one of these is taken as an undefined term in geometry?
a) Angle
b) Triangle
c) Line
d) Square
Answer:
c) Line – Along with point and plane, line is considered undefined.
Question 7. A plane surface, according to Euclid, is defined as:
a) A flat area with volume
b) A surface which lies evenly with straight lines on itself
c) A surface bounded by a curve
d) Any two-dimensional figure
Answer:
b) A surface which lies evenly with straight lines on itself.
Question 8. Euclid’s Axiom 1 states:
a) Things which are equal to the same thing are equal to one another
b) If equals are subtracted from equals, remainders are equal
c) The whole is greater than the part
d) All right angles are equal
Answer:
a) Things which are equal to the same thing are equal to one another.
Question 9. Euclid’s Axiom 5 states:
a) If equals are added to equals, wholes are equal
b) The whole is greater than the part
c) All right angles are equal
d) Two circles with equal radii are equal
Answer:
b) The whole is greater than the part.
Question 10. Which of the following is Euclid’s Postulate 1?
a) A line segment can be extended indefinitely
b) A straight line may be drawn from any one point to any other point
c) A circle can be drawn with any centre and radius
d) All right angles are equal
Answer:
b) A straight line may be drawn from any one point to any other point.
Question 11. According to Euclid’s Postulate 2, a terminated line can be:
a) Measured exactly
b) Produced indefinitely
c) Divided into equal parts only
d) Compared with angles
Answer:
b) Produced indefinitely – Postulate 2 states this.
Question 12. Which postulate allows us to draw a circle with any centre and radius?
a) Postulate 1
b) Postulate 2
c) Postulate 3
d) Postulate 4
Answer:
c) Postulate 3 – A circle can be drawn with any centre and any radius.
Question 13. Postulate 4 states that:
a) A line has infinite points
b) All right angles are equal to one another
c) The whole is greater than the part
d) A triangle can be formed on any line
Answer:
b) All right angles are equal to one another.
Question 14. Which of Euclid’s postulates is considered the most complex?
a) Postulate 1
b) Postulate 2
c) Postulate 3
d) Postulate 5
Answer:
d) Postulate 5 – It concerns intersecting lines and interior angles.
Question 15. According to Axiom 5.1, given two distinct points:
a) Multiple lines pass through both
b) No line passes through both
c) Only one unique line passes through them
d) A circle passes through them
Answer:
c) Only one unique line passes through them.
Question 16. Euclid’s fifth postulate deals with:
a) Parallel lines
b) Circle construction
c) Measurement of areas
d) Right angles
Answer:
a) Parallel lines – It establishes when two lines will intersect.
Question 17. The principle of superposition is based on which axiom?
a) Axiom 1
b) Axiom 4
c) Axiom 5
d) Postulate 3
Answer:
b) Axiom 4 – Things which coincide with one another are equal.
Question 18. Which axiom justifies that halves of the same thing are equal?
a) Axiom 6
b) Axiom 7
c) Postulate 2
d) Postulate 4
Answer:
b) Axiom 7 – States that things which are halves of the same things are equal.
Question 19. Euclid deduced a total of how many propositions in his Elements?
a) 200
b) 365
c) 465
d) 500
Answer:
c) 465 – He used axioms, postulates, and reasoning to deduce them.
Question 20. Theorem 5.1 states that two distinct lines:
a) Can have infinite common points
b) Cannot have more than one point in common
c) Must be parallel
d) Must intersect in a circle
Answer:
b) Cannot have more than one point in common.
Question 21. If AB = PQ and PQ = XY, then according to Axiom 1:
a) AB > XY b) AB = XY – Things equal to the same thing are equal.
b) AB = XY
c) AB < XY
d) AB + XY = 0
Answer:
Question 22. Which civilization used geometry mainly for practical purposes like constructing pyramids?
a) Indians
b) Babylonians
c) Egyptians
d) Greeks
Answer:
c) Egyptians – They applied geometry for land and construction.
Question 23. The ratio of length : breadth : thickness of Indus Valley bricks was:
a) 2:4:1
b) 4:2:1
c) 1:2:4
d) 1:4:2
Answer:
b) 4:2:1 – This ratio was used in Harappa and Mohenjo-Daro.
Question 24. In the construction of altars in ancient India, which shapes were used?
a) Only squares
b) Only circles
c) Rectangles, triangles, trapeziums
d) Hexagons
Answer:
c) Rectangles, triangles, trapeziums – Various shapes were combined.
Question 25. The Sriyantra from the Atharvaveda consists of how many subsidiary triangles?
a) 9
b) 27
c) 43
d) 81
Answer:
c) 43 – Formed by interwoven isosceles triangles.
Question 26. Which Greek mathematician is credited with the first known proof?
a) Pythagoras
b) Thales
c) Euclid
d) Archimedes
Answer:
b) Thales – Proved that a circle is bisected by its diameter.
Question 27. Euclid’s fifth postulate involves angles whose sum is less than:
a) 90°
b) 120°
c) 180°
d) 360°
Answer:
c) 180° – Interior angles on the same side less than two right angles.
Question 28. If equals are added to equals, the wholes are ___.
a) Greater
b) Equal
c) Unequal
d) Different
Answer:
b) Equal – This is Euclid’s Axiom 2.
Question 29. Which axiom implies that everything equals itself?
a) Axiom 4
b) Axiom 1
c) Axiom 5
d) Axiom 7
Answer:
a) Axiom 4 – Things which coincide with one another are equal.
Question 30. Euclid’s system of geometry is based on which type of reasoning?
a) Inductive
b) Deductive
c) Approximate
d) Experimental
Answer:
b) Deductive – Conclusions are drawn logically from assumptions.
Question 31. According to Euclid’s Postulate 5, if a line falls on two straight lines and interior angles are less than 180°, the lines:
a) Are parallel
b) Meet on that side
c) Never meet
d) Are perpendicular
Answer:
b) Meet on that side – Provided the sum is less than two right angles.
Question 32. The geometry developed in Babylon and Egypt was mostly:
a) Practical
b) Theoretical
c) Abstract
d) Modern
Answer:
a) Practical – It was applied to construction and measurement.
Question 33. The geometry of Greece was mainly focused on:
a) Practical construction
b) Deductive reasoning and proofs
c) Mensuration only
d) Volume computation
Answer:
b) Deductive reasoning and proofs – Greeks emphasized logical reasoning.
Question 34. Euclid’s Postulate 2 is equivalent to saying that a line segment can be extended to form a ___.
a) Ray
b) Line
c) Circle
d) Angle
Answer:
b) Line – A terminated line can be produced indefinitely.
Question 35. Which of the following is considered a universal truth rather than a geometric postulate?
a) The whole is greater than the part
b) A circle can be drawn with any centre and radius
c) All right angles are equal
d) A terminated line can be extended
Answer:
a) The whole is greater than the part – This is a universal axiom.
Fill in the blanks on Introduction to Euclid’s Geometry for Class 9 Maths
1. The word ‘geometry’ is derived from the Greek words ‘geo’ meaning earth and ‘metrein’ meaning ___.
Answer:
to measure
2. Euclid is known as the ‘Father of Geometry’ and his famous treatise is called ___.
Answer:
Elements
3. According to Euclid, a point is defined as that which has ___.
Answer:
no part
4. According to Euclid, a line is defined as a ___ length.
Answer:
breadthless
5. The ends of a line are called ___.
Answer:
points
6. A plane surface is defined by Euclid as one which lies evenly with ___ on itself.
Answer:
straight lines
7. According to Euclid’s Axiom 1, things which are equal to the same thing are ___ to one another.
Answer:
equal
8. Euclid’s Axiom 2 states: If equals are added to equals, the wholes are ___.
Answer:
equal
9. According to Euclid’s Axiom 3, if equals are subtracted from equals, the remainders are ___.
Answer:
equal
10. Euclid’s Axiom 5 states: The ___ is greater than the part.
Answer:
whole
11. Euclid’s Postulate 1: A ___ may be drawn from any one point to any other point.
Answer:
straight line
12. Euclid’s Postulate 2: A terminated line can be ___ indefinitely.
Answer:
produced
13. Euclid’s Postulate 3 allows a ___ to be drawn with any centre and any radius.
Answer:
circle
14. According to Euclid’s Postulate 4, all ___ angles are equal to one another.
Answer:
right
15. Euclid’s fifth postulate is also known as the ___ postulate.
Answer:
parallel
16. Euclid’s fifth postulate says that if a line intersects two lines and the interior angles on the same side are less than ___, the lines will meet on that side.
Answer:
180°
17. According to Euclid’s Axiom 4, things which coincide with one another are ___.
Answer:
equal
18. According to Euclid’s Axiom 7, things which are halves of the same thing are ___.
Answer:
equal
19. Theorem 5.1 states that two distinct lines cannot have more than ___ point in common.
Answer:
one
20. Euclid deduced a total of ___ propositions in his treatise Elements.
Answer:
465
21. The geometry developed in Greece was mainly based on ___ reasoning.
Answer:
deductive
22. The geometry used in ancient Egypt and Babylon was largely ___ in nature.
Answer:
practical
