If a transversal intersects two lines in such a way that a pair of consecuitive interior angles are supplementary; then two lines are parallel.

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

If a Transversal intersects two lines in such a way that a pair of alternate interior angles are 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 6.5 : If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel,then prove that the two lines are parallel.

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

Fill in the blanks in each of the following to make the statement true: (i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are.... (ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are... (iii) Two lines perpendicular to the same line are.... to each other. (iv) Two lines parallel to the same line are .......... to each other. (v) If a transversal intersects a pair of lines in such away that a pair of alternate angles are equal, then the line are... (vi) If a transversal intersects a pair of lines in such away that the sum of interior angles on the same side of transversal is 180,then the line are .......

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

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

Transversal to two parallel lines: