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
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