Angles made by a Transversal

Write the converse of, "if the corresponding angles formed by a transversal of two lines are congruent, then two lines are parallel."

If the bisectors of a pair of alternate angles formed by a transversal with two given lines are parallel,prove that the given lines are parallel.

If the bisectors of a pair of corresponding angles formed by a transversal with two given lines lines are parallel, prove that the given lines are parallel.

If two parallel lines are cut by a transversal, then the alternate interior angles are equal

If two parallel lines are intersected by a transversal,prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles.

If two parallel lines are intersected by a transversal,prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles.

If two parallel lines intersected by a transversal , then name the pair of angles formed that 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 three or more parallel lines are intersected by two transversal; Prove that the intercepts made by them on tranversal are propotional.