x=7
Explanation
As the triangles are similar
[tex]\begin{gathered} AC=DF \\ AB=DE \\ BC=EF \end{gathered}[/tex]
in the same way, the angles are the same
so
[tex]\begin{gathered} m\measuredangle C=m\measuredangle F \\ \text{replace} \\ 2x+14=4x \\ \text{solve for x} \\ \text{subtract 2x in both sides} \\ 2x+14-2x=4x-2x \\ 14=2x \\ \text{divide both sides by 2} \\ \frac{14}{2}=\frac{2x}{2} \\ 7=x \end{gathered}[/tex]
Hence, when x= 7 the triangles are congruent.
the sides have 2 sides at common and one side, so
[tex]\text{SAS}[/tex]
I hope this helps you
