Question

Show that the two triangles ABC and DEF are congruent by the HL theorem.

Answer 1

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:

$\overline {AC} \cong \overline {DF}$, $\overline{BC} \cong \overline {EF}$

$AC = DF, BC = EF$

$\sqrt{AB^{2}+BC^{2}} = \sqrt{DE^{2}+EF^{2}}$, $BC = EF$

If we know that $AB = 10$, $BC = 4$, $DE = 10$ and $EF = 4$, then we have the following outcomes:

$\sqrt{10^{2}+4^{2}} = \sqrt{10^{2}+4^{2}}$

$4 = 4$

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: brainly.com/question/21972776