To prove two triangles congruent,
We use SSS Criteria – Side Side Side Criteria
In SSS Congruency Criteria,
- All 3 sides of both triangles are equal
For example
Here,
All 3 corresponding sides are equal.
So, the triangles must be congruent
Let’s take some examples
Are these triangles congruent?
In ∆ABC and ∆EDF,
AB = ED ( Both 6 cm )
BC = DF ( Both 7 cm )
AC = EF (Both 8 cm )
∴ ∆ABC ≅ ∆EDF ( SSS Congruence Rule)
Here,
A ⟷ E
B ⟷ D
C ⟷ F
Are these triangles congruent?
In ∆ABC and ∆QPR,
AB = QP ( Both 14 cm)
BC = PR ( Both 15 cm )
AC = QR ( Both 21 cm )
∴ ∆ABC ≅ ∆QPR (SSS Congruence Rule)
Here,
A ⟷ Q
B ⟷ P
C ⟷ R
Are these triangles congruent?
In ∆DEF and ∆NML,
DE = NM ( Both 3.2 cm )
EF = ML (Both 3 cm )
DF = NL ( Both 3.5 cm )
∴ ∆DEF ≅ ∆NML ( SSS Congruence Rule)
Here,
D ⟷ N
F ⟷ L
E ⟷ M
Are these triangles congruent?
In ∆ABC and ∆QRP,
AC = QP ( Both 5 cm )
BC = RP ( Both 4cm )
AB ≠ QR
Since all sides are not equal,
∴ ∆ABC ≇ ∆QRP
Are these triangles congruent?
In ∆ADB and ∆ADC,
AD = AD ( Common )
AB = AC (Both 3.5 cm)
DB = DC (Both 2.5 cm)
∆ADB ≅ ∆ADC (SSS Congruence Rule)
Here,
A ⟷ A
B ⟷ C
D ⟷ D
In Fig, AB =AC and D is the mid-point of (BC) ̅.
(i)State the three pairs of equal parts in ∆ADB and ∆ADC.
(ii)Is ∆ADB ≅ ∆ADC? Give reasons.
(iii)Is ∠B = ∠C? Why?
In ∆ADB and ∆ADC,
AD = AD ( Common )
AB = AC ( Given )
DB = DC ( D is the mid – point of BC )
∴ ∆ADB ≅ ∆ADC ( SSS Congruence Rule )
Also,
∠B = ∠C (By CPCT)
Here,
A ⟷ A
B ⟷ C
D ⟷ D
In Fig, AC = BD and AD = BC. Which of the following statements is meaningfully written?
(i)∆ABC ≅ ∆ABD
(ii)∆ABC ≅ ∆BAD
In ∆ABC and ∆BAD,
AB = AB (Common )
AC = BD (Given )
AD = BC (Given )
∴ ∆ABC ≅ ∆BAD ( SSS Congruence Rule)
Here,
A ⟷ B
C ⟷ D
B ⟷ A
Hence (ii) is correct
