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Theorem 7.6 - Class 9 - Angle opposite to larger side is larger. - Theorems

Theorem 7.6 - Chapter 7 Class 9 Triangles - Part 2
Theorem 7.6 - Chapter 7 Class 9 Triangles - Part 3

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Transcript

Theorem 7.6 :- If two sides of a triangle are unequal, the angle opposite to larger side is larger ( or greater ). Given :- ∆ABC such that AB > AC . To Prove :- ∠C > ∠B . Construction:- Take a point P on AB such that AP = AC and join CP. Let ∠APC = x° & ∠BCP = y° Proof:- Since AP = AC ⇒ ∠ACP = ∠APC ⇒ ∠ACP = x On line AB, ∠APC + ∠BPC = 180° ∠BPC = 180° − ∠APC ∠BPC = 180° − x In Δ PBC, ∠BPC + ∠PBC + ∠PCB = 180° 180° − 𝑥 + ∠PBC + 𝑦 = 180° ∠PBC = 180° − 180° + 𝑥 − 𝑦 ∠PBC = 𝑥 − 𝑦 ∠B = 𝑥 − 𝑦 Now, ∠C = ∠BPC + ∠PCA = 𝑥 + 𝑦 Thus, ∠C > ∠B Similarly, If AB > BC , Take point Q on AB such that BQ = BC, then we can prove ∠C > ∠A Hence Proved.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.