Question

in the triangles, \\( \overline { b c } \cong \overline { d e } \\) and \\( \overline { a c } \cong \overline { f e } \\). if \\( m \angle c \\) is greater than \\( m \angle e \\), then \\( \overline { a b } \\) is \\( \overline { d f } \\). 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, but the included angle of the first triangle is larger than the included angle of the second triangle, then the side opposite the larger included angle is longer.

Step2: Identify the sides and angles

We are given that \(BC\cong DE\) and \(AC\cong FE\). The included angles are \(\angle C\) and \(\angle E\), and we know \(m\angle C>m\angle E\). The sides opposite these angles are \(AB\) and \(DF\) respectively.

Step3: Apply the Hinge Theorem

By the Hinge Theorem, since \(BC = DE\), \(AC = FE\) and \(m\angle C>m\angle E\), we can conclude that \(AB>DF\).

Answer:

longer than