Question

Which triangles are congruent according to the SAS criterion ?

Answer 1

$\triangle \mathrm{ABC}, \triangle \mathrm{FGE}$ and $\Delta \mathrm{PQR}$

Step-by-step explanation:

Step 1: Take the pair of triangles ABC and FGE.

In $\triangle \mathrm{ABC}$ and $\triangle \mathrm{FGE}$,

AB = FG (Side)

$\angle\mathrm{CAB}=\angle \mathrm{EFG}$ (Angle)

AC = EF (Side)

$\therefore \triangle \mathrm{ABC} \cong \Delta \mathrm{FGE}$ (by SAS congruence criterion) – – – – – (1)

Step 2: Take the pair of triangles FGE and PQR.

In $\Delta \mathrm{FGE} \text { and } \Delta \mathrm{PQR}$,

FG = PQ (Side)

$\angle\mathrm{EFG}=\angle \mathrm{RPQ}$ (Angle)

EF = PR (Side)

$\therefore \triangle \mathrm{FGE} \cong \Delta \mathrm{PQR}$ (by SAS congruence criterion) – – – – – (2)

Step 3: To find congruent triangles by SAS criterion.

From (1) and (2) we can conclude that,

$\therefore \Delta \mathrm{ABC} \cong \Delta \mathrm{FGE} \cong \Delta \mathrm{PQR}$ (by SAS congruence criterion)

Hence, $\triangle \mathrm{ABC}, \triangle \mathrm{FGE} \text { and } \Delta \mathrm{PQR}$ are congruent according to the SAS criterion.