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]