Congruency of triangles

Chapter 7 Class 7 Congruence of Triangles
Concept wise

Let suppose two triangles are congruent

We know that two triangles are congruent when

• They have same shape
• They have same size

Let’s rotate PQR

And super impose ∆ABC & ∆PQR

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

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?

Then,

 Corresponding angles are equal Corresponding sides are equal ∠M = ∠Z MN = ZX ∠N = ∠X NO = XY ∠O = ∠Y OM = YZ

Here,

M ⟷ Z

N ⟷ X

O ⟷ Y

So,

∆MNO ≅ ∆ZXY

### Which triangles are congruent?

Then,

 Corresponding angles are equal Corresponding sides are equal ∠P = ∠U PR = US ∠R = ∠S QR = TS ∠Q = ∠T PQ = UT

Here,

P ⟷ U

R ⟷ S

Q ⟷ T

So,

∆PQR ≅ ∆UTS

### Which triangles are congruent?

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

Here,

R ⟷ S

P ⟷ U

Q ⟷ T

∴ ∆PQR ≅  ∆UTS

Here,

Y ⟷ K

Z ⟷ J

X ⟷ L

So, ∆XYZ ≅  ∆LKJ

Here,

A ⟷ Y

B ⟷ X

C ⟷ Z

So, ∆ABC ≅  ∆YXZ

Here,

J ⟷ N

I ⟷ L

K ⟷ M

So, ∆IJK ≅ ∆LNM

Here,

P ⟷ U

Q ⟷ S

R ⟷ T

So, ∆PQR ≅ ∆UST

### Which triangles are congruent?

Here,

N ⟷ D

O ⟷ F

M ⟷ E

So, ∆MNO ≅ ∆EDF

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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.