Question

1. in this figure, $\triangle afc\cong\triangle efc$. which statement must be true? $\overline{ad}\perp\overline{eb}$ $\overline{cf}\perp\overline{ae}$ $\overline{eb}\perp\overline{ca}$ $\overline{ad}\perp\overline{ce}$

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle AFC\cong\triangle EFC\), then \(\angle AFC=\angle EFC\).

Step2: Analyze the sum of angles

We know that \(\angle AFC+\angle EFC = 180^{\circ}\) (linear - pair of angles).

Step3: Calculate the measure of angles

If \(\angle AFC=\angle EFC\) and \(\angle AFC+\angle EFC = 180^{\circ}\), then \(\angle AFC=\angle EFC = 90^{\circ}\).

Answer:

\(\overline{CF}\perp\overline{AE}\)