Question

From the figures, find which correspondence between the triangles is a congruence :

Answer 1

HEY ,__________________↓↓↓

① IN ∆ABC & ∆ DEF

AB = DE
BC = EF
AC = DF

∴ ∆ABC ≈ ∆DEF(S.S.S.)

② IN ∆DEF & PQR

EF = QR
∠E = ∠Q
DF = PR

∴ ∆DEF ≈ ∆ PQR(R.H.S.)

③ IN ∆DEF & ∆PQR

EF = PQ
∠DEF = ∠PQR
∠DFE = ∠QPR

∴ ∆ DEF ≈ ∆PQR(A.S.A)

HOPE IT HELPS ☺☺✌

Answer 2

Hi ,

1 ) From figure ( a ) ,

In ∆ABC and ∆DEF

AB = DE ( s )

BC = EF ( s )

CA = FD ( s )

Therefore ,

∆ABC is congruent to ∆DEF

( SSS criterion )

2 ) From figure ( b ) ,

In ∆FED and ∆PQR

<FED = <PQR = 90° [ R ] Right angle

FD = PR ( H ) Hypotenuse

EF = PQ ( S ) Side

Therefore ,

∆FED congruent to ∆PQR

( RHS criterion )

3 ) from figure ( c ),

In ∆DFE and ∆ RQP

<DFE = <PQR = 40° ( A )

FE = QP ( S )

<DEF = <RPQ = 80° ( A )

Therefore ,

∆DEF congruent to ∆PQR

( SAS criterion )

I hope this helps you.

: )