Question

Read the following statements which are taken as axioms :
1) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
2) If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent ? Justify your answer.

Answer 1

Dear Friend,
This system of axioms are not consistent.1) When two parallel sides are intersected by a transversal, then corresponding angles are always equal. Here,∠1=∠5,∠2=∠6,∠4=∠8and ∠7=∠32) The alternate interior angles will be always equal in parallel lines.