Corresponding parts of congruent triangle (CPCT)

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,

Let’s check more examples

Which triangles are congruent?

Then,

Here,

M ⟷ Z

N ⟷ X

O ⟷ Y

So,

  ∆MNO ≅ ∆ZXY

Which triangles are congruent?

Then,

Here,

P ⟷ U

R ⟷ S

Q ⟷ T

So,

  ∆PQR ≅ ∆UTS

Which triangles are congruent?

Then,

Here,

Q ⟷ N

R ⟷ M

P ⟷ L

So,

  ∆PQR ≅ ∆LNM

Which triangles are congruent?

Here,

R ⟷ S

P ⟷ U

Q ⟷ T

∴ ∆PQR ≅  ∆UTS

Which triangles are congruent?

Here,

Y ⟷ K

Z ⟷ J

X ⟷ L

So, ∆XYZ ≅  ∆LKJ

Which triangles are congruent?

Here,

A ⟷ Y

B ⟷ X

C ⟷ Z

So, ∆ABC ≅  ∆YXZ

Which triangles are congruent?

Here,

J ⟷ N

I ⟷ L

K ⟷ M

So, ∆IJK ≅ ∆LNM

Which triangles are congruent?

Here,

P ⟷ U

Q ⟷ S

R ⟷ T

So, ∆PQR ≅ ∆UST

Which triangles are congruent?

Here,

N ⟷ D

O ⟷ F

M ⟷ E

So, ∆MNO ≅ ∆EDF