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

45.jpg

Here,

  2 sides and the angle between  them are equal.

 

Let’s do some examples

 

Are these triangles congruent?

SAS Congruency Criteria - Part 2

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?

SAS Congruency Criteria - Part 3

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?

SAS Congruency Criteria - Part 4

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?

SAS Congruency Criteria - Part 5

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?

SAS Congruency Criteria - Part 6

 

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

SAS Congruency Criteria - Part 7

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

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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.