To prove two triangles congruent,

  We can also use AAS criteria – Angle Angle Side

 

This criteria is equivalent to ASA Criteria.

 

Here’s how:

Suppose we are given two triangles Δ ABC & Δ PQR

64.jpg

 

Let’s prove this by ASA congruency finding ∠A & ∠P

In ∆ABC,

In ∆PQR ,

By Angle Sum Property,

∠A + ∠B + ∠C = 180°

∠A + 40° + 80° = 180°

∠A + 120° = 180°

∠A = 180° − 120°

∠A = 60°         

By Angle Sum Property,

∠P + ∠Q + ∠R = 180°

∠P + 40° + 80° = 180°

∠P + 120° = 180°

∠P = 180° − 120°

∠P = 60°         

 

64.jpg

Now, In ∆ABC and ∆PQR,

  ∠A = ∠P           (Both are 60°)

  AC = PR           (Given )

  ∠C = ∠R           (Both are 80°)

∴ ∆ABC ≅ ∆PQR     (ASA congruence rule)

 

OR

 

We can prove this by AAS

  In ∆ABC and ∆PQR

  ∠B = ∠Q        (Both are 40°)

  ∠C = ∠R        (Both are 80°)

  AC = PR         ( Given )

∴ ∆ABC ≅ ∆PQR      (AAS congruence rule)

 

  1. Chapter 7 Class 7 Congruence of Triangles
  2. Concept wise
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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.