Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.12210203322.jpg

Step 1
To make the triangle congruent by using the SAS congruence,
First naming the edges and vertex of the triangle,

Step 2
By using sum of interior angle property in ${\displaystyle \mathrm{△}ABC\text{and}\mathrm{△}DEF}$,
${\displaystyle \mathrm{\angle }ABC={180}^{\circ }-(\mathrm{\angle }ABC+\mathrm{\angle }BAC)}$
${\displaystyle \mathrm{\angle }DEF={180}^{\circ }-(\mathrm{\angle }EDF+\mathrm{\angle }DFE)}$
it is given that,
${\displaystyle \mathrm{\angle }ACB=\mathrm{\angle }EDF={90}^{\circ }}$ (given)...(i)
${\displaystyle \mathrm{\angle }BAC=\mathrm{\angle }DFE\left(given\right)}$...(ii)
Adding equation (i) and (ii) and subtracting them form ${\displaystyle {180}^{\circ }}$ in both sides,
${\displaystyle {180}^{\circ }-(\mathrm{\angle }ACB+\mathrm{\angle }BAC)={180}^{\circ }-(\mathrm{\angle }EDF+\mathrm{\angle }DFE)}$
${\displaystyle \mathrm{\angle }ABC=\mathrm{\angle }DEF}$
Now, in ${\displaystyle \mathrm{△}ABC\text{and}\mathrm{△}DEF}$,
AB=EF(given)
${\displaystyle \mathrm{\angle }ABC=\mathrm{\angle }DEF}$(Proved above)
BC=DE(given)
${\displaystyle \mathrm{△}ABC\stackrel{\sim }{=}\mathrm{△}DEF}$ (By SAS Congruence Theorem)
Yes, the provided information is enough to prove the triangle congruent by SAS.