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

2 Theorem 6.3 - Class 9 - Thus for lines AB and CD .jpg

  1. Chapter 6 Class 9 Lines and Angles
  2. Serial order wise
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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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