Question

determining logical progression in proot
analyze the figure and the two - column proof.
which statement/reason pair can be used when proving \\( \overline { fc } \cong \overline { eb } \\)?

Explanation:

Step1: Recall triangle congruence

To prove \( \overline{FC}\cong\overline{EB}\), we use CPCTC (Corresponding Parts of Congruent Triangles are Congruent). So we need to prove the triangles \( \triangle AFC\) and \( \triangle DEB\) are congruent.

Step2: Check given information

We have \( AF\cong ED\) (given), \( \angle AFC\cong\angle DEB\) (all right angles are congruent), and \( AC\cong BD\) (from steps 1 - 8 in the proof). By the Hypotenuse - Leg (HL) congruence criterion for right - triangles (if we consider right - triangles \( \triangle AFC\) and \( \triangle DEB\), where \(AF\) and \(ED\) are legs, \(AC\) and \(BD\) are hypotenuses), \( \triangle AFC\cong\triangle DEB\).

Answer:

\(\triangle DEB\cong\triangle AFC\)