Chapter 5 Introduction to Euclid’s Geometry Assertation & Reasoning Questions Class 9th Mathematics

1) Assertion: There can be infinite number of lines that can be drawn through a single point.

Reason: . from this point we can draw only two lines.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: c) Assertion is true but reason is false.

2) Assertion: Through two distinct points there can be only one line that can be drawn.

Reason: . . From this two point we can draw only one line

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: a) Assertion and reason are correct and reason is correct explanation for Assertion.

3) Assertion: According to Euclid’s 1st axiom- “Things which are equal to the same thing are also equal to one another”.

Reason:  if AB = PQ and PQ = XY, then AB = XY

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

4) Assertion: If two circles are equal, then their radii are equal.

Reason: The circumference and the centre of both the circles coincide; and thus, the radius of the two circles should be equal.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

5) Assertion: Parallel lines are those lines which never intersect each other

Reason: Parallel lines can be two or more lines.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

6) Assertion:  A dimensionless dot which is drawn on a plane surface is known as point.

Reason: A point is that which has no part.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

7) Assertion: : A collection of points that has only length and no breadth is known as a line

Reason: the line segment cannot be extended from both sides.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion.

8) Assertion: A collection of points that has only length and no breadth is known as a line

Reason: line can be extended from both side

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

9) Assertion: The whole is always greater than the part.

Reason: A cake when it is whole or complete, assume that it measures 2 pounds but when a part from it is taken out and measured, its weigh will be smaller than the previous measurement.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans:a) Assertion and reason are correct and reason is correct explanation for Assertion.

10) Assertion: A figure formed of line segments only is called a rectilinear figure.

Reason: A circle is a rectilinear figure.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: c) Assertion is correct but reason is false.

11) Assertion: The line drawn from the center of the circle to any point on its circumference is called radius of a circle

Reason: the line from any point on the circumference of the circle to the center of the circle is known as diameter of a circle

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: c) Assertion is true but reason is false.

12) Assertion: Euclid’s fifth postulate does imply the existence of the parallel lines.

Reason: If the sum of the interior angles is equal to the sum of the right angles, then the two lines will not meet each other at any given point, hence making them parallel to each other.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: c) Assertion is true but reason is false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: c) Assertion is true but reason is false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

14) Assertion: , if AB = CD, then AC = BD.

Reason: above statement we can prove by Euclid axiom 2 equals are added to equals, then the wholes are equal.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for Assertion.

15) Assertion: it is given that AD=BC. Then AC =BD

Reason: above line we can prove by Euclid axiom 3 If equals are subtracted from equals, the remainders are equal.”

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for Assertion.

16) Assertion: If A, B and C are any three points on a line and B lies between A and C  then prove that AB + BC = AC.

Reason: Euclid’s axiom 4, states that things which coincide with one another are equal to one another.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

17) Assertion: A Greek mathematician, thales is credited with giving the first known proof.

Reason: The first known proof that ‘the rectangle is bisected by its diameter was given by Pythagoras

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false.

Ans: c) assertion is correct but reason is false.

18) Assertion: 3 + 7 = 9 is a statement.

Reason: A sentence that can be judged to be true or false, but not both, is called a statement.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

19) Assertion: According to Euclid’s second axiom, when equals. are added to equals, the wholes are equal.

Reason: Ram and Ravi have the same weight. If they each gain weight by 2 kg, second Euclid’s axiom will be used to compare their weights?

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is  correct explanation for Assertion

20) Assertion:  Euclid’s fifth postulate imply the existence of parallel lines.

Reason: The sum of the interior angles will be equal to sum of the two right angles then two lines will not meet each other on either sides and therefore they will be parallel to each other.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

21) Assertion: If lines AB ,AC ,AD and AE are parallel to line l , the point A,B,C,D,E are collinear.

Reason : infinite line can be drawn through A and parallel to l.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: c) Assertion is true but reason is false

22) Assertion:  An infinite number of lines can be drawn to pass through a given point.

Reason: A line segment has two end-points.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

23) Assertion: The locus of points which is at a same distance from single point is called as ellipse

Reason: two lines are said to be perpendicular when angle between them is 80°

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: d) both Assertion and reason are false

24) Assertion: Boundaries of surfaces are curves.

Reason: surfaces are dimensional figures and their boundaries are one-dimensional which curves are.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion