Which triangles are congruent according to the SAS criterion ?

Question

asked Apr 2, 2021 206k views

2 Answers

Jacob Murphy · Answer 1 · 2021-04-09T07:01:19+0000

$\triangle \mathrm{ABC}, \triangle \mathrm{FGE}$ 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.