Q. 35.0( 3 Votes )

# Read the following statements which are taken as axioms:

(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.

(ii) If a transversal intersects two parallel lines, then alternate interior angles are equal.

Is this system of axioms consistent? Justify your answer.

Answer :

A system of axiom is called consistent, if there is no statement which can be deduced from these axioms such that it contradicts any axioms.

We know that, if a transversal intersects two parallel line, then each pair of corresponding angles are equal, which is a theorem. So, statement (i) is false and not an axiom.

Also, we know that, if a transversal intersects two parallel line, then each pair of alternate interior angles are equal. It is also a theorem. So, statement(ii) is true and an axiom.

Thus, in given statements, first is false and second is an axiom.

Hence, given of axioms is not consistent.

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PREVIOUSStudy the following statement:“Two intersecting lines cannot be perpendicular to the same line”.Check whether it is an equivalent version to the Euclid’s fifth postulate.[Hint: Identify the two intersecting lines l and m and the line n in the above statement.]NEXTRead the following two statements which are taken as axioms:(i) If two lines intersect each other, then the vertically opposite angles are not equal.(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°.Is this system of axioms consistent? Justify your answer.

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