Suppose, we have two triangles

 

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To prove ∆ABC ≅ ∆PQR,

We use different congruency criteria

 

They are

  • SSS – Side Side Side
  • SAS − Side Angle Side
  • ASA – Angle Side Angle
  • AAS − Same as ASA
    • AAA – Angle Angle Angle
  • RHS − Right-angle Hypotenuse side

 

Let’s discuss them

 

SSS

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In ∆ABC & ∆PQR

  AB = PQ                (Both are 5)

  BC = QR               (Both are 4)

  AC = PR               (Both are 3)

∴ ∆ABC ≅ ∆PQR   (SSS Congruence Rule)

 

For more details,

Please check SSS Explanation (link) & proof (link)

31.jpg

 

Note :

Here ∆ABC ∆PQR

   not ∆ABC ∆QRP

Order of writing the triangle is important

 

SAS

32.jpg

In ∆ABC & ∆PQR

  AB = PQ                  ( Both are 5 )

  ∠B  = ∠Q                 ( Both are 60° )

  BC = QR                 ( Both are 4 )

∴ ∆ABC ≅ ∆PQR    ( SAS Congruence Rule )

 

For more details,

Please check SAS Explanation (link) & proof (link)

 

 

ASA

33.jpg

In ∆ABC & ∆PQR

  ∠B = ∠Q         ( Both are 40 °)

  BC  = QR       ( Both are 5 cm )

  ∠C = ∠R        ( Both are 80 °) 

∴ ∆ABC ≅ ∆PQR

 

For more details,

Please check ASA Explanation (link) & proof (link)

 

RHS

35.jpg

 

 

In ∆ABC & ∆PQR

 

∠B = ∠Q      ( Right angle, both 90 °)

  AC  = PR    ( Hypotenuse, both 5 cm )

  AB = PQ     (Side , both 4 cm )

 ∴ ∆ABC ≅ ∆PQR        ( RHS Congruency rule )

 

For more details,

Please check RHS Explanation (link) & proof (link)

 

  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.