CBSE Class 9 Mathematics Introduction to Euclid's Geometry MCQs Set 16

Multiple Choice Questions (MCQs) for Class 9 Mathematics: Introduction to Euclid's Geometry

Review structured MCQ sets for Class 9 Mathematics Introduction to Euclid's Geometry. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Practice Introduction to Euclid's Geometry MCQs for Class 9 Mathematics

View or download the dedicated Introduction to Euclid's Geometry MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: Given two distinct points, the number of lines that can pass through both of them is
(a) exactly one
(b) many
(c) none
(d) exactly two
Show Answer & Explanation

Answer: (a) exactly one

Explanation:
1. Euclid's first postulate says a straight line can be drawn from any point to any other point.
2. Two distinct points fix exactly one line, so there are not 'many' lines through them.

Teacher's Note:
1. Two points determine a line.

Question 2: If \( P,Q,R \) are three points on a line and \( Q \) lies between \( P \) and \( R \), then
(a) \( PR+RQ=PQ \)
(b) \( PQ+QR=PR \)
(c) \( RP+QR=PQ \)
(d) \( PQ=PR+QR \)
Show Answer & Explanation

Answer: (b) \( PQ+QR=PR \)

Explanation:
1. \( Q \) divides \( PR \) into the two parts \( PQ \) and \( QR \), so the parts add up to the whole.
2. \( PQ+QR=PR \).

Teacher's Note:
1. The whole segment is the sum of its parts.

Question 3: If a point \( Q \) lies between \( P \) and \( R \) with \( PQ=QR \), then \( Q \) is called
(a) a line segment
(b) the end point of PR
(c) the mid-point of PR
(d) a collinear point only
Show Answer & Explanation

Answer: (c) the mid-point of PR

Explanation:
1. A point of a segment that is equidistant from the two ends is its mid-point.

Teacher's Note:
1. Equal distances from both ends.

Question 4: Every line segment has
(a) two mid-points
(b) no mid-point
(c) infinitely many mid-points
(d) one and only one mid-point
Show Answer & Explanation

Answer: (d) one and only one mid-point

Explanation:
1. The point at distance half the length from an end is unique, so a segment has exactly one mid-point.

Teacher's Note:
1. Half the length gives one point.

Question 5: A part of a line with two end points is called a
(a) line segment
(b) ray
(c) line
(d) point segment
Show Answer & Explanation

Answer: (a) line segment

Explanation:
1. A line extends without end both ways; a part with two ends is a line segment.

Teacher's Note:
1. Count the end points.

Question 6: A part of a line with one end point is called a
(a) line segment
(b) ray
(c) line
(d) angle
Show Answer & Explanation

Answer: (b) ray

Explanation:
1. A ray starts at one point and goes on endlessly in one direction.

Teacher's Note:
1. One end point means a ray.

Question 7: Three or more points lying on the same line are called
(a) non-collinear points
(b) concurrent points
(c) collinear points
(d) parallel points
Show Answer & Explanation

Answer: (c) collinear points

Explanation:
1. Points on a common line are collinear.

Teacher's Note:
1. Co means together, linear means line.

Question 8: Three or more points that do not lie on the same line are called
(a) collinear points
(b) concurrent points
(c) coincident points
(d) non-collinear points
Show Answer & Explanation

Answer: (d) non-collinear points

Explanation:
1. If no single line passes through all of them, they are non-collinear.

Teacher's Note:
1. The opposite of collinear.

Question 9: According to Euclid's third postulate,
(a) a circle can be drawn with any centre and any radius
(b) all right angles are equal
(c) a terminated line can be produced indefinitely
(d) equals added to equals give equal wholes
Show Answer & Explanation

Answer: (a) a circle can be drawn with any centre and any radius

Explanation:
1. The third postulate is the one about drawing circles; the others describe lines, right angles and the common notions.

Teacher's Note:
1. Postulates 1 to 5 are about lines, circles and angles.

Question 10: If two circles are equal, then their radii are
(a) unequal
(b) equal
(c) double of each other
(d) half of each other
Show Answer & Explanation

Answer: (b) equal

Explanation:
1. Equal circles coincide when placed one on the other, so their radii coincide and are equal.

Teacher's Note:
1. Equal circles have equal radii (and conversely).

Question 11: The distance of a point from a line is
(a) the length of any segment from the point to the line
(b) the length of the longest segment to the line
(c) the length of the perpendicular from the point to the line
(d) the length of the line
Show Answer & Explanation

Answer: (c) the length of the perpendicular from the point to the line

Explanation:
1. The perpendicular is the shortest segment from a point to a line, and this length is the distance.

Teacher's Note:
1. Distance means shortest distance.

Question 12: Things which coincide with one another are
(a) unequal to one another
(b) double of one another
(c) parallel to one another
(d) equal to one another
Show Answer & Explanation

Answer: (d) equal to one another

Explanation:
1. This is Euclid's fourth common notion (axiom 4).

Teacher's Note:
1. Think of placing one figure on the other.

Question 13: Axioms or postulates are the _____ which are obvious universal truths.
(a) assumptions
(b) theorems
(c) definitions
(d) constructions
Show Answer & Explanation

Answer: (a) assumptions

Explanation:
1. They are accepted without proof; they are not proved like theorems.

Teacher's Note:
1. Axioms are not proved.

Question 14: If equals are added to equals, the _____ are equal.
(a) parts
(b) wholes
(c) halves
(d) differences
Show Answer & Explanation

Answer: (b) wholes

Explanation:
1. Euclid's second axiom: if equals are added to equals, the wholes are equal.

Teacher's Note:
1. Add equal quantities to both sides.

Question 15: If equals are subtracted from equals, the _____ are equal.
(a) wholes
(b) doubles
(c) remainders
(d) sums
Show Answer & Explanation

Answer: (c) remainders

Explanation:
1. Euclid's third axiom: if equals are subtracted from equals, the remainders are equal.

Teacher's Note:
1. Subtract equal quantities from both sides.

Question 16: All _____ angles are equal to one another.
(a) acute
(b) obtuse
(c) straight
(d) right
Show Answer & Explanation

Answer: (d) right

Explanation:
1. This is Euclid's fourth postulate (all right angles are equal).

Teacher's Note:
1. Fourth postulate.

Question 17: The number of lines that pass through two distinct points is
(a) one
(b) two
(c) three
(d) infinite
Show Answer & Explanation

Answer: (a) one

Explanation:
1. Through two distinct points exactly one straight line passes.

Teacher's Note:
1. Unique line.

Question 18: Two distinct lines cannot have more than _____ point in common.
(a) two
(b) one
(c) three
(d) zero
Show Answer & Explanation

Answer: (b) one

Explanation:
1. If two lines shared two points, they would be the same line, so distinct lines meet in at most one point.

Teacher's Note:
1. Two points fix a line.

Question 19: A _____ is that which has no part.
(a) line
(b) surface
(c) point
(d) plane
Show Answer & Explanation

Answer: (c) point

Explanation:
1. Euclid's first definition: a point is that which has no part.

Teacher's Note:
1. No length, breadth or thickness.

Question 20: The ends of a line are
(a) lines
(b) surfaces
(c) angles
(d) points
Show Answer & Explanation

Answer: (d) points

Explanation:
1. Euclid defined the ends of a line to be points.

Teacher's Note:
1. A line is breadthless length.

Question 21: The whole is _____ the part.
(a) greater than
(b) less than
(c) equal to
(d) half of
Show Answer & Explanation

Answer: (a) greater than

Explanation:
1. Euclid's fifth common notion: the whole is greater than the part.

Teacher's Note:
1. The whole contains the part and more.

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Introduction to Euclid's Geometry Objective Questions & Solutions for Class 9 Mathematics

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FAQs

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