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

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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°         

 

AAS Congruence rule - Part 2

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)

 

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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.