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.
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.
Rate this question :
In the given figure, it is given that AC=BD,
Prove that AB=CD.
RS Aggarwal & V Aggarwal - Mathematics