Read 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.
We know that, if two lines intersect each other, then the vertically opposite angles are equal. It is a theorem, So given Statement I is false and not
an axiom.
Also, we know that, if a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°. It is ah axiom. So, given Statement II
is true and an axiom.
Thus, in given statements, first is false and second is an axiom. Hence, given system of axioms is not consistent.
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