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