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Anu01 jain
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Asked: 2023-03-24T11:41:56+00:00 In:

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 Figure). Show that: (i) Δ APB ≅ Δ AQB (ii) BP = BQ or B is equidistant from the arms of ∠ A.

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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 Figure). Show that: (i) Δ APB ≅ Δ AQB (ii) BP = BQ or B is equidistant from the arms of ∠ A.

Which contradicts the definition of a point on the angle bisector.
How to corresponding parts of congruent triangles are congruent
9th Maths EXERCISE 7.1,Page No:118, Questions No:5
NCERT Books for Session 2023-2024 are based on CBSE Board.

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      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 Figure). Show that: (i) Δ APB ≅ Δ AQB (ii) BP = BQ or B is equidistant from the arms of ∠ A.

      (i) In ΔAPB and ΔAQB,
      ∠APB = ∠AQB [∵ Each 90°]
      ∠PAB = ∠QAB [∵ Line l bisects angle A]
      AB = AB [∵ Common]
      Hance, ΔAPB ≅ ΔAQB [∵ ASA Congruency Rule]

      (ii) BP = BQ [∵ Corresponding parts of congruent Triangles are equal ]

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