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

37.jpg

Here,

  All 3 corresponding sides are equal.

 

So, the triangles must be congruent

 

Let’s take some examples

 

Are these triangles congruent?

38.jpg

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?

39.jpg

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?

40.jpg

 

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?

41.jpg

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?

42.jpg

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?

 

43.jpg

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

44.jpg

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

 

  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.