Question

applying the converse of the hinge theorem. given $overline{ac}congoverline{fe}$ and $overline{cb}congoverline{ed}$ which statement is correct? angle a is larger than angle b. angle c is congruent to angle e. angle c is smaller than angle e. angle c is larger than angle e.

Explanation:

Step1: Recall converse of Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle, and the third - side of the first triangle is longer than the third - side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.

Step2: Identify sides and angles

In \(\triangle ABC\) and \(\triangle FDE\), we have \(\overline{AC}\cong\overline{FE}\), \(\overline{CB}\cong\overline{ED}\), and \(AB = 15\) in, \(FD=11\) in. The included angles for the congruent sides are \(\angle C\) and \(\angle E\). Since \(AB>FD\), by the converse of the Hinge Theorem, \(\angle C>\angle E\).

Answer:

Angle C is larger than angle E.