Theorem 7.1 (ASA Congruency) Class 9 - If 2 angles and side are equal.jpg

2 Theorem 7.1 BC = EF PBC DEF (SAS Congruence rule ).jpg
3 Theorem 7.1 if AB  DE, then by chosing point M on DE such that AB = ME and.jpg

  1. Chapter 7 Class 9 Triangles
  2. Serial order wise

Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.