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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 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.