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 (Check Why AAA is not a congruence )
  • RHS − Right-angle Hypotenuse side

 

Let’s discuss them

 

SSS

Criteria for congruency of triangles - Part 2

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  & proof

Criteria for congruency of triangles - Part 3

 

Note :

Here ∆ABC ∆PQR

   not ∆ABC ∆QRP

Order of writing the triangle is important

 

SAS

Criteria for congruency of triangles - Part 4

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  & proof

 

 

ASA

Criteria for congruency of triangles - Part 5

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 & proof

 

RHS

Criteria for congruency of triangles - Part 6

 

 

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  & proof

 

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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.