NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry (Ex 5.2) Exercise 5.2

1. How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Ans: Euclid’s fifth postulate states that a straight line falling on two another straight lines, will make the interior angle on the same side of it and it is taken together less than two right angles, i.e., ${180^ \circ }$, then, if the two straight lines are being produced indefinitely, then, they will be meeting on that side, where the sum of angles will be less than two right angles.

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In other words, it can be represented as:

If, $\angle 1 + \angle 2 < {180^ \circ }$

Then, the lines AB and CD are going to meet at left side of the line PQ.

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Now, if $\angle 1 + \angle 2 = {180^ \circ }$

Then the lines AB and CD are not going to intersect each other. And the intersecting line PQ would be perpendicular to lines AB and CD.

Therefore, we can say that the two distinct intersecting lines will not be parallel to the same line.

2. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

Ans: As per Euclid's fifth postulate if a straight line falls on two straight lines and if the interior angles on the same side of that line is less then sum of two right angles then if the two lines are extended indefinitely, then the lines will meet on the side which the sum of the angles is less than two right angles (${180^ \circ }$).

If the sum of interior angles on one side of line is equal to two right angles, then the two lines are said to be parallel lines.

It can be explained from the figures given below:

• According to Euclid’s 5th postulate, when $n$ line falls on lines $l$ and $m$, and if $\angle 1 + \angle 2 < {180^ \circ }$ , then $\angle 3 + \angle 4 > {180^ \circ }$. Producing line on lines $l$ and $m$ further, they will meet on the side of $\angle 1$ and $\angle 2$ which is less than ${180^ \circ }$.

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• If $\angle 1 + \angle 2 = {180^ \circ }$ , then $\angle 3 + \angle 4 = {180^ \circ }$.

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The lines $l$ and $m$, are not going to meet either at the side of $\angle 1$ and $\angle 2$ or at the side of $\angle 3$ and $\angle 4$.

In the above figure, for two the lines $l$ and $m$, sum of interior angles is equal to two right angles (${180^ \circ }$). Hence, they are parallel lines and will not meet each other on either side of line $n$.

• Therefore, we can say that Euclid’s fifth postulate implies existence of parallel lines.

NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry Exercise 5.2

Opting for the NCERT solutions for Ex 5.2 Class 9 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 5.2 Class 9 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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