Euclid’s fifth postulate is
a. The whole is greater than the part
b. A circle may be described with any centre and any radius
c. All right angles are equal to one another
d. 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

Solution:

We know that

Euclid’s fifth postulate is “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”.

Therefore, Euclid's fifth postulate is “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”.

✦ Try This: Solve the equation c - 6 = 12 and state which axiom do you use here.

Given, the equation is c - 6 = 12

We have to solve the equation and state which axiom is used here.

Using Euclid’s second axiom,

If equals are added to the equals, the wholes are equal.

On adding 6 on both the sides of the equation,

c - 6 + 6 = 12 + 6

c = 12 + 6

c = 18

Therefore, the solution of the equation is c = 18.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5

NCERT Exemplar Class 9 Maths Exercise 5.1 Sample Problem 2

Euclid’s fifth postulate is a. The whole is greater than the part, b. A circle may be described with any centre and any radius, c. All right angles are equal to one another, d. 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

Summary:

Postulate was used for a universal truth specific to geometry. Euclid’s fifth postulate is that 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

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