Question

in the triangles, $overline{bc}congoverline{de}$ and $overline{ac}congoverline{fe}$. if $mangle c$ is greater than $mangle e$, then $overline{ab}$ is ______ $overline{df}$. congruent to longer than shorter than the same length as

Explanation:

Step1: Recall the Hinge - Theorem

The Hinge - Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

Step2: Identify congruent sides and angles

In \(\triangle ABC\) and \(\triangle DFE\), we have \(\overline{BC}\cong\overline{DE}\) and \(\overline{AC}\cong\overline{FE}\). The included angles for these pairs of sides are \(\angle C\) and \(\angle E\) respectively. Given that \(m\angle C>m\angle E\).

Answer:

B. longer than