Theorem 7.1 (ASA Congruence Rule) :- Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. Given :- ABC and DEF such that B = E & C = F and BC = EF To Prove :- ABC DEF Proof:- We will prove by considering the following cases :- Case 1: Let AB = DE In ABC and DEF AB = DE B = E BC = EF ABC DEF Case 2: AB > DE Construction :- Take a point P on AB such that PB = DE In PBC and DEF PB = DE B = E BC = EF PBC DEF PCB = DFE But ACB = DFE Thus, ACB = PCB This is possible only if P is coincides with A AB = DE By Case 1 ABC DEF Case 3: If AB < DE If AB < DE, then by choosing a point M on DE such that AB = ME and repeating the argument in Case (2). We get ABC DEF

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.