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Asked: 2023-03-28T03:45:39+00:00 In:

ΔABC is an isosceles triangle in which AB = AC.Side BA is produced to D such that AD = AB (see Figure). Show that ∠ BCD is a right angle.

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ΔABC is an isosceles triangle in which AB = AC.Side BA is produced to D such that AD = AB (see Figure). Show that ∠ BCD is a right angle.

Prove the observe angle.
define the supplementary to angle
Class 9th Maths, Page No:124, Questions No:6, Exercise 7.2
Triangles Solutions for Class 9th Maths, Session 2023-2024.

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      ΔABC is an isosceles triangle in which AB = AC.Side BA is produced to D such that AD = AB (see Figure). Show that ∠ BCD is a right angle.

      In ΔACD,
      AB = AC [∵ Given]
      ∠ACD = ∠D …(1) [∵ Angles opposite to equal sides are equal]
      In ΔABC,
      AB = AC [∵ Given]
      ∠B = ∠ACB …(2) [∵ Angles opposite to equal sides are equal]
      In ΔDBC,
      ∠D + ∠B + ∠BCD = 180°
      ⇒ ∠ACD + ∠ACB + BCD = 180° [∵ From the equation (1) and (2)]
      ⇒ ∠BCD + ∠BCD = 180° [∵ ∠ACD + ∠ACB = ∠BCD]
      ⇒ 2∠BCD = 180°
      ⇒ ∠BCD = (180°/2) = 90°
      Hence, ∠BCD is a is a right angle.

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