35. Exemplar Exercise Problems XVIII

1. 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 intersect two parallel lines, then alternate interior angles are equal. Is this system of axioms consistent? Justify your answer. 

 

2. 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.