Question

determining side length relationships. given $overline{ac}congoverline{fe}$ and $overline{cb}congoverline{ed}$ which statement is correct? ab = fd, ab < fd, ab > fd, ab ≤ fd

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 the given information

We are given that $\overline{AC}\cong\overline{FE}$ and $\overline{CB}\cong\overline{ED}$. The included angle in $\triangle ABC$ is $\angle C = 83.5^{\circ}$, and the included angle in $\triangle FED$ is $\angle E=62.7^{\circ}$. Since $83.5^{\circ}>62.7^{\circ}$.

Step3: Apply the Hinge - Theorem

By the Hinge - Theorem, the side opposite the larger included angle is longer. In $\triangle ABC$, the side opposite $\angle C$ is $AB$, and in $\triangle FED$, the side opposite $\angle E$ is $FD$. So $AB > FD$.

Answer:

AB > FD