Question

Which triangles are congruent according to the SAS criterion ?

Answer 1

E

Explanation:

Answer 2

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

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.