Question

I will give brainliest to best answer

Answer 1

That's a Congruent Triangle question.

The first thing that we should to analize is it: What figure is EFGH? The question say for us that $\overline{EF} \cong \overline{GH}$ and $\overline{EH} \cong \overline{GF}$, therefore, EFGH is a parallelogram because its parallel sides are congruents (equals).

Now, we should to proof that $\triangle EFH \cong \triangle GHF$. The simbol "≅" means congruence, that is, $\triangle EFH \cong \triangle GHF$ means that the triangles EFH and GHF are equals.

Let's proof:

$\overline{HF}$ is a diagonal of the parallelogram EFGH. When we have a diagonal in a parallelogram, the opposite angles are congruents (look at the picture: the blue angles are congruent and the red angles are congruents too). Therefore, $E\hat{F}H \cong F\hat{H}G$ and $E\hat{H}F \cong H\hat{F}G$.

Both triangle has a comum side: the diagonal $\overline{HF}$. The diagonal $\overline{HF}$ is between two angles that we know that are congruents, Therefore, by the case ASA (Angle, Side, Angle), we proof that $\triangle EFH \cong \triangle GHF$.