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.
Given :- Two lines AB and CD.
And transversal PS intersecting AB at Q and CD at R,
Such that alternate interior angles are equal.
i.e, BQR = CRQ
To Prove :- AB CD
Proof :-
For lines AB & PS
AQP = BQR
But, BQR = CRQ
From (1) & (2),
AQP = CRQ
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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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