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  • Write whether the following statements are True or False? Justify your answer: Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

Write whether the following statements are True or False? Justify your answer:

Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

Answers (1)

True

Solution:

Euclid’s fifth postulate: if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

It means that if the sum of angles ÐA and ÐB in the figure is less than the sum of two right angles then A, B meet on the same side of angle A and B continued indefinitely.

All attempts to prove the fifth postulate as a theorem led to great achievement in the creation of several other geometries. These geometries are different from Euclidean geometry and called non-Euclidean geometry.

Hence the given statement is true.

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