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Theorem 6.3 - Class 9 - If alternate angles are equal, lines parallel..jpg

Theorem 6.3 - Chapter 6 Class 9 Lines and Angles - Part 2

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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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.