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