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Theorem 6.2 - Class 9th - Alternate interior angles are equal. - Parallel lines and traversal - Properties

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  1. Chapter 6 Class 9 Lines and Angles
  2. Serial order wise
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Theorem 6.2 :- If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal. Given :- Two parallel lines AB and CD. Let PS be the transversal intersecting AB at Q and CD at R. To Prove :- Each pair of alternate interior angles are equal. i.e, ∠ BQR = ∠ CRQ and ∠ AQR = ∠ QRD Proof :- First, we will prove ∠ BQR = ∠ CRQ From (1) and (2) ∠ BQR = ∠ CRQ Similarly we can prove ∠ AQR = ∠ QRD Hence, pair of alternate interior angles are equal. Hence proved.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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