[tex]\triangle \mathrm{ABC}, \triangle \mathrm{FGE}[/tex] and [tex]\Delta \mathrm{PQR}[/tex]
Step-by-step explanation:
Step 1: Take the pair of triangles ABC and FGE.
In [tex]\triangle \mathrm{ABC}[/tex] and [tex]\triangle \mathrm{FGE}[/tex],
AB = FG (Side)
[tex]\angle\mathrm{CAB}=\angle \mathrm{EFG}[/tex] (Angle)
AC = EF (Side)
[tex]\therefore \triangle \mathrm{ABC} \cong \Delta \mathrm{FGE}[/tex] (by SAS congruence criterion) – – – – – (1)
Step 2: Take the pair of triangles FGE and PQR.
In [tex]\Delta \mathrm{FGE} \text { and } \Delta \mathrm{PQR}[/tex],
FG = PQ (Side)
[tex]\angle\mathrm{EFG}=\angle \mathrm{RPQ}[/tex] (Angle)
EF = PR (Side)
[tex]\therefore \triangle \mathrm{FGE} \cong \Delta \mathrm{PQR}[/tex] (by SAS congruence criterion) – – – – – (2)
Step 3: To find congruent triangles by SAS criterion.
From (1) and (2) we can conclude that,
[tex]\therefore \Delta \mathrm{ABC} \cong \Delta \mathrm{FGE} \cong \Delta \mathrm{PQR}[/tex] (by SAS congruence criterion)
Hence, [tex]\triangle \mathrm{ABC}, \triangle \mathrm{FGE} \text { and } \Delta \mathrm{PQR}[/tex] are congruent according to the SAS criterion.
