Let suppose two triangles are congruent

12.jpg

We know that two triangles are congruent when

  • They have same shape
  • They have same size

 

Let’s rotate PQR

14.jpg

And super impose ∆ABC & ∆PQR

15.jpg

 

So,

Points match

  A ⟷ P

  B ⟷ Q

  C ⟷ R

 

Thus, we write

  ∆ABC ≅ ∆PQR

 

Not

     ∆ABC ≅ ∆QRP

     ∆ABC ≅ ∆PRQ

 

Because, in

  ∆ABC ≅ ∆PQR

A ⟷ P

B ⟷ Q

C ⟷ R

 

But, why is this order important?

Because of CPCT,

  CPCT is corresponding parts of Congruent Triangles

 

If two triangles are congruent,

  • Their corresponding sides are equal
  • Their corresponding angles are equal

 

Now,

  In ∆ABC & ∆PQR

16.jpg

If ∆ABC ≅ ∆PQR

Then,

Corresponding angles are equal

Corresponding sides are equal

∠A = ∠P

AB = PQ 

∠B = ∠Q 

BC = QR 

∠C = ∠R 

AC = PR

 

Let’s check more examples

Which triangles are congruent?

18.jpg

Then,

Corresponding angles are equal

Corresponding sides are equal

∠M = ∠Z MN = ZX
∠N = ∠X NO = XY
∠O = ∠Y OM = YZ

 

19.jpg

 

Here,

M ⟷ Z

N ⟷ X

O ⟷ Y

So,

  ∆MNO ≅ ∆ZXY

 

Which triangles are congruent?

20.jpg

Then,

Corresponding angles are equal

Corresponding sides are equal

∠P = ∠U PR = US
∠R = ∠S QR = TS
∠Q = ∠T PQ = UT

21.jpg

Here,

P ⟷ U

R ⟷ S

Q ⟷ T

 

So,

  ∆PQR ≅ ∆UTS

 

Which triangles are congruent?

22.jpg

Then,

Corresponding angles are equal

Corresponding sides are equal

∠P = ∠L PQ = LN
∠Q = ∠N QR = NM
∠R = ∠M PR = LM

 

Here,

Q ⟷ N

R ⟷ M

P ⟷ L

 

So,

  ∆PQR ≅ ∆LNM

 

Which triangles are congruent?

23..jpg

Here,

R ⟷ S

P ⟷ U

Q ⟷ T

 

∴ ∆PQR ≅  ∆UTS

 

Which triangles are congruent?

24.jpg

Here,

Y ⟷ K

Z ⟷ J

X ⟷ L

 

So, ∆XYZ ≅  ∆LKJ

 

Which triangles are congruent?

25.jpg

Here,

A ⟷ Y

B ⟷ X

C ⟷ Z

 

So, ∆ABC ≅  ∆YXZ

 

Which triangles are congruent?

26.jpg

 

Here,

J ⟷ N

I ⟷ L

K ⟷ M

 

So, ∆IJK ≅ ∆LNM

 

Which triangles are congruent?

27.jpg

Here,

P ⟷ U

Q ⟷ S

R ⟷ T

 

So, ∆PQR ≅ ∆UST

 

Which triangles are congruent?

28.jpg

Here,

N ⟷ D

O ⟷ F

M ⟷ E

 

So, ∆MNO ≅ ∆EDF

  1. Chapter 7 Class 7 Congruence of Triangles
  2. Concept wise
Ask Download

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.