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Anu01 jain
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Asked: 2023-03-25T03:59:21+00:00 In:

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that (i) ΔABD ≅ ΔBAC (ii) BD = AC (iii) ∠ABD = ∠BAC.

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ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that (i) ΔABD ≅ ΔBAC (ii) BD = AC (iii) ∠ABD = ∠BAC.

Pairs of congruent sides and angles, respectively.
Corresponding angles are congruent.
Class 9th, EXERCISE 7.1, Page No: 118.
Questions No:2.
NCERT Book, Chapter TRIANGLES Question Answer.
Session 2023-2024 are based on CBSE Board.

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    1. Best Answer
      ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that (i) ΔABD ≅ ΔBAC (ii) BD = AC (iii) ∠ABD = ∠BAC.

      In ΔABD and ΔBAC,
      AD = BC [∵ Given]
      ∠DAB = ∠CAB [∵ Given]
      AB = AB [∵ Common]
      Hance, ΔABD ≅ ΔBAC [∵ SAS Congruency Rule]
      (ii) BC = BD [∵ Corresponding parts of congruent triangles are equal]
      (iii) ∠ABD = ∠BAC [∵ Corresponding parts of congruent triangles are equal]

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