Theorem 6.5 :-
If a transversal intersects two lines, such that the pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.
Given :- Two parallel lines AB and CD and a transversal PS intersecting AB at Q and CD at R
such that BQR + DRQ = 180
To Prove :- AB CD.
Proof :-
For lines PS
DRQ + DRS = 180
But, BQR + DRQ = 180
From (1) & (2)
DRQ + DRS = BQR + DRQ
DRS = BQR
But they are corresponding angles.
Thus, for lines AB & CD with transversal PS, corresponding angles are equal
Hence AB and CD are parallel.
Hence proved

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.