in the triangles, $\overline{bc} \cong \overline{de}$ and $\overline{ac} \cong \overline{fe}$. if $m\angle c$ is greater than $m\angle e$, then $\overline{ab}$ is $____$ $\overline{df}$.
options:
congruent to
longer than
shorter than
the same length as

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# Brief Explanations:
The problem involves triangles with two pairs of equal sides ($\overline{AC} \cong \overline{FE}$ and $\overline{BC} \cong \overline{DE}$) and a comparison of the included angles ($m\angle C > m\angle E$). By the Hinge Theorem (SAS Inequality Theorem), if two sides of one triangle are congruent to two sides of another triangle, the triangle with the larger included angle has the longer third side. Here, the third sides are $\overline{AB}$ (opposite $\angle C$) and $\overline{FD}$ (opposite $\angle E$). Since $m\angle C > m\angle E$, $\overline{AB}$ is longer than $\overline{FD}$.

# Answer:
longer than

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