Question

analyze the figure and the two - column proof
which statement/reason pair can be used when proving ( overline{fc}congoverline{eb} )?

Explanation:

Step1: Identify right triangles

We have $\triangle AFC$ and $\triangle DEB$ which are right - angled triangles ($\angle AFC\cong\angle DEB = 90^{\circ}$)

Step2: Identify congruent hypotenuses

From the proof, we know that $\overline{AC}\cong\overline{BD}$ (hypotenuses of the right - angled triangles $\triangle AFC$ and $\triangle DEB$)

Step3: Identify congruent legs

We are given that $\overline{AF}\cong\overline{ED}$ (legs of the right - angled triangles $\triangle AFC$ and $\triangle DEB$)

Step4: Apply Hypotenuse - Leg Congruence Theorem

Since in right - angled triangles $\triangle AFC$ and $\triangle DEB$, $\overline{AC}\cong\overline{BD}$ (hypotenuses) and $\overline{AF}\cong\overline{ED}$ (legs), by the Hypotenuse - Leg ($HL$) Congruence Theorem, $\triangle AFC\cong\triangle DEB$. Then, by the Corresponding Parts of Congruent Triangles are Congruent ($CPCTC$) property, $\overline{FC}\cong\overline{EB}$

Answer:

$\triangle AFC\cong\triangle DEB$; Hypotenuse - Leg Congruence Theorem