Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.
The Hypotenuse-Leg theorem states that two right triangles are congruent if and only if their hypotenuses and any of their corresponding legs are congruent. That is to say:
[tex]\overline {AC} \cong \overline {DF}[/tex], [tex]\overline{BC} \cong \overline {EF}[/tex]
[tex]AC = DF, BC = EF[/tex]
[tex]\sqrt{AB^{2}+BC^{2}} = \sqrt{DE^{2}+EF^{2}}[/tex], [tex]BC = EF[/tex]
If we know that [tex]AB = 10[/tex], [tex]BC = 4[/tex], [tex]DE = 10[/tex] and [tex]EF = 4[/tex], then we have the following outcomes:
[tex]\sqrt{10^{2}+4^{2}} = \sqrt{10^{2}+4^{2}}[/tex]
[tex]4 = 4[/tex]
Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.
We kindly invite to check this question on triangles: https://brainly.com/question/21972776
