Question

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.

Answer 1

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.