Which triangles are congruent according to the sas

Ответ:

LuckyCharms988

15.01.2022

Mathematics

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

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Ответ:

natalie2sheffield

29.02.2020

Mathematics

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{bases}{parallel~sides}\\ h=height\\[-0.5em] \hrulefill\\ a=29\\ h=9\\ A=193.5 \end{cases}\implies 193.5=\cfrac{9(29+b)}{2} \\\\\\ 387=9(29+b)\implies \cfrac{387}{9}=29+b\implies 43=29+b\implies 14=b$

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Which triangles are congruent according to the sas criterion ?

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