Ex 7.1, 5 - Line l is bisector of angle A and B is any point - Ex 7.1

  1. Chapter 7 Class 9 Triangles
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Ex7.1, 5 Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that: (i) ΔAPB ≅ ΔAQB (ii) BP = BQ or B is equidistant from the arms of ∠A. Given: l is the bisector of ∠ A So, ∠PAB = ∠QAB BP & BQ are perpendiculars from B, So, ∠APB = ∠AQB = 90° To prove: (i) ΔAPB ≅ ΔAQB (ii) BP = BQ Proof: In ΔAPB and ΔAQB, ∠APB = ∠AQB ∠PAB = ∠QAB AB = AB ∴ ΔAPB ≅ ΔAQB ∴ BP = BQ Hence proved

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