Given triangle ABC with side lengths;
[tex]\begin{gathered} AB=14 \\ BC=8 \\ AC=10.4 \end{gathered}[/tex]If triangle ABC is congruent to triangle DEF, then it means;
[tex]\begin{gathered} \Delta ABC\cong\Delta DEF \\ \text{Hence,} \\ AB\cong DE \\ BC\cong EF \\ AC\cong DF \end{gathered}[/tex]For the triangles to be congruent, then there must be a similar ratio that exists between all three sides of both triangles. This means, for instance, if one side of triangle ABC is dilated by a factor of 2 to get the length of the corresponding side in triangle DEF, the same factor must apply to the remaining two sides.
Therefore, from the options provided;
[tex]\begin{gathered} \text{Option F} \\ \frac{14}{28}=\frac{1}{2},\frac{8}{20}=\frac{2}{5},\frac{10.4}{20.8}=\frac{1}{2} \\ \text{Not Correct} \end{gathered}[/tex][tex]\begin{gathered} \text{Option G} \\ \frac{14}{35}=\frac{2}{5},\frac{8}{16}=\frac{1}{2},\frac{10.4}{20.8}=\frac{1}{2} \\ \text{Not correct} \end{gathered}[/tex][tex]\begin{gathered} Option\text{ H} \\ \frac{14}{28}=\frac{1}{2},\frac{8}{20}=\frac{2}{5},\frac{10.4}{26}=\frac{2}{5} \\ \text{Not correct} \end{gathered}[/tex][tex]\begin{gathered} Option\text{ J} \\ \frac{14}{35}=\frac{2}{5},\frac{8}{20}=\frac{2}{5},\frac{10.4}{26}=\frac{2}{5} \\ \text{Correct} \end{gathered}[/tex]ANSWER:
Option J is the correct answer.
This is because all the three sides of triangle ABC which are 14, 8 and 10.4 when multiplied by a factor of 5/2 would yield the sides 35, 20 and 26 for the other triangle DEF.
This is not true for the other options F, G and H.
