Check sibling questions

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?

SSS Congruency Criteria - Part 2

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?

SSS Congruency Criteria - Part 3

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?

SSS Congruency Criteria - Part 4

 

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?

SSS Congruency Criteria - Part 5

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?

SSS Congruency Criteria - Part 6

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?

 

SSS Congruency Criteria - Part 7

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

SSS Congruency Criteria - Part 8

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

 

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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.