To prove two triangles congruent,

We use SAS Criteria – Side Angle Side

In SAS Congruency Criteria,

- 2 sides of both the triangles are equal
- 1 angle between these side of both the triangles are equal.

__
For example
__

__
__

Here,

2 sides and the angle between them are equal.

Let’s do some examples

###
**
Are these triangles congruent?
**

**
**

In ∆ABC and ∆FED,

BC = ED
*
(Both are 10 cm
*
*
)
*

∠C = ∠D
*
(Both are 45
*
*
°)
*

AC = FD
*
(
*
*
Both are 8 cm
*
*
)
*

∴ ∆ABC ≅ ∆FED
*
(SAS Congruence Rule)
*

Here,

C⟷D

A⟷F

B⟷E

###
**
Are these triangles congruent?
**

**
**

In ∆PQR and ∆UTS,

PR = US
*
(Both are 20 cm
*
*
)
*

∠R = ∠S
*
(Both are 15
*
*
°)
*

QR = TS
*
(Both are 10 cm
*
*
)
*

∴ ∆PQR ≅ ∆UTS
*
(SAS Congruence Rule)
*

Here,

R⟷S

P⟷U

Q⟷T

###
**
Are these triangles congruent?
**

**
**

In ∆ABC and ∆RQP,

AC = RP
*
(
*
*
Both are 2.5 cm
*
*
)
*

∠C = ∠P
*
(
*
*
Both are 35
*
*
°)
*

BC = QP
*
(
*
*
Both are 3 cm
*
*
)
*

∴ ∆ABC ≅ ∆RQP
*
(
*
*
SAS Congruence Rule
*
*
)
*

Here,

C⟷P

A⟷R

B⟷Q

###
**
Are these triangles congruent?
**

**
**

In ∆DEF and ∆RPQ,

EF = PQ
*
(Both are 3 cm
*
*
)
*

∠F = ∠Q
*
(Both are 40
*
*
°)
*

DF = RQ
*
(Both are 3.5 cm
*
*
)
*

∴ ∆DEF ≅ ∆RPQ
*
(SAS Congruence Rule
*
*
)
*

Here,

F⟷Q

D⟷R

E⟷P

###
**
Are these triangles congruent?
**

**
**

In ∆PRS and ∆RPQ,

RS = PQ
*
(
*
*
Both are 3.5 cm
*
*
)
*

∠R = ∠P
*
(Both are 30
*
*
°)
*

PR = RP
*
(Common
*
*
)
*

∴ ∆PRS ≅ ∆RPQ
*
(
*
*
SAS Congruence Rule)
*

Here,

P⟷R

S⟷Q

R⟷P

####
**
In the following diagram:-
**

In Fig, AB and CD bisect each other at O.

(i) State the three pairs of equal parts in two triangles AOC and BOD.

(ii) Which of the following statements are true?

(a) ∆AOC ≅ ∆DOB

(b) ∆AOC ≅ ∆BOD

In ∆AOC and ∆BOD,

OA = OB
*
(Given
*
*
)
*

∠AOC = ∠BOD
*
(Vertically opposite angles)
*

OC = OD
*
(
*
*
Given)
*

∴ ∆AOC ≅ ∆BOD
*
(
*
*
SAS Congruence Rule
*
*
)
*

Here,

A⟷B

O⟷O

C⟷D