Theorem 6.2 : If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

If a transversal intersects two parallel lines, then prove that each pair of alternate interior angles is equal.

If a transversal intersects two parallel lines; then each of alternate interior angles are equAL.

Theorem 6.3 : If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.

Theorem 6.3 : If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.

Theorem 6.4 : If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.

Theorem 6.4 : If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.

If a transversal intersects two parallel lines; then each pair of consecutive interior angles are supplementary.

If a transversal intersects two parallel lines, then alternate interior angles have one common _______

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.

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.