. Prove that if two parallel lines are intersected by a transversal
Prove that if two parallel lines are intersected by a transversal, then prove that the bisectors of the interior angles form a rectangle.
We are given two parallel lines AB and CD and a transversal EF intersect them at G and H respectively. GM, HM, GL and HL are the bisectors of the two pairs of interior angles.
We have to prove that GMHL is a rectangle.
So, GMHL is a parallelogram.
Hence, GMHL is a rectangle.
Therefore, we have proved the given statement.