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Asked: 2023-03-28T03:47:04+00:00 In:

In Figure sides AB and AC of Δ ABC are extended to points P and Q respectively. Also, ∠ PBC AB.

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In Figure sides AB and AC of Δ ABC are extended to points P and Q respectively. Also, ∠ PBC AB.

Define the exterior angle and consider triangles.
NCERT Books for Session 2022-2023 are based on CBSE Board.
Important Triangles Solutions for class 9th.
Important NCERT Book, Exercise 7.4, Question no: 2, Page No: 132.

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      In Figure sides AB and AC of Δ ABC are extended to points P and Q respectively. Also, ∠ PBC AB.

      ∠PBC + ∠ABC = 180° [∵ Linear Pair]
      ⇒ ∠PBC = 180° – ∠ABC …(1)
      Similarly,
      ∠QCB + ∠ACB = 180° [∵ Linear pair]
      ⇒∠QCB = 180° – ∠ACB …(2)
      Given that:
      ∠PBC > ∠QCB
      ⇒ 180° – ∠ABC – ∠ACB
      ⇒ ∠ABC > ∠ACB …(3)
      In ΔABC,
      ∠ABC > ∠ACB [∵ From the equation (3)]
      Hence, AC > AB [∵ In a triangle, greater angle has longer side opposite to it]

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