Theorem 6.5 - Class 9 - If interior angles are supplementary, lines.jpg

2 Theorem 6.5 - Class 9 - Hence AB and CD are Parallel hence Proved.jpg


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

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

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Davneet Singh
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