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
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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 :- Δ ABC and Δ 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.