Correct Answer - Option 4 : 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.
Concept:
All five postulate of Euclid's are as follow:
First: A straight line segment can be drawn by joining any two points.
Second: Any straight line segment can be extended indefinitely through both ends.
Third: Given any straight line segment we can draw a circle having line segment as radius and one end point of line segment as center of circle.
Fourth: All right angles are equal to each other.
Fifth: If two lines are drawn which intersect a third line in such a way that the sum of the inner angles on one side is less than two right angles (\(180^\circ\)), then the two lines must intersect each other in that side where sum of angles is less than right angles.
Calculation:
1. All right angles are equal to one another- Euclid's Fourth postulate
2. A circle may be described with any center and any radius- Euclid's Third postulate
3. The whole is greater than the part- Euclid's Fifth axiom
4. 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- Euclid's Fifth postulate
