Question

12 in this figure, △afc≅△efc. which statement must be true?
○ eb⊥ca
○ ad⊥ce
○ ad⊥eb
○ cf⊥ae

Explanation:

Step1: Recall properties of congruent triangles

If $\triangle AFC\cong\triangle EFC$, then corresponding parts are equal. And the line - segment $CF$ is common to both triangles. Since the two triangles are congruent, $\angle AFC=\angle EFC$.

Step2: Analyze angle - sum

$\angle AFC+\angle EFC = 180^{\circ}$ (linear - pair of angles). Since $\angle AFC=\angle EFC$, then $\angle AFC=\angle EFC = 90^{\circ}$.

Step3: Determine perpendicularity

By the definition of perpendicular lines (if the angle between two lines is $90^{\circ}$, the lines are perpendicular), we have $\overline{CF}\perp\overline{AE}$.

Answer:

$\overline{CF}\perp\overline{AE}$