Suppose, we have two triangles
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
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
Note :
Here ∆ABC ≅ ∆PQR
not ∆ABC ≅ ∆QRP
Order of writing the triangle is important
SAS
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
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
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