Question

Given: $\overline{\text{FC}}$ and $\overline{\text{SH}}$ bisect each other at $\text{A;}$localid="1638250328146" $\text{FC}=\text{SH}$.

Prove: $\text{SA}=\text{AC}$.

Short answer

It is proved that$\overline{AC}=\overline{SA}$.

Step-by-step solution

Step 1. Consider the diagram.

Here, $\overline{FC}$,$\overline{SH}$ bisect each other $A$ and$\overline{FC}=\overline{SH}$

Step 2. State the proof.

As $\overline{FC}$, $\overline{SH}$ bisect each other $A$,

$\overline{AC}=\frac{1}{2}\left(\overline{FC}\right)$and $\overline{SA}=\frac{1}{2}\left(\overline{SH}\right)$

Also,

$\overline{FC}=\overline{SH}$(Given)

Multiply both sides by $\frac{1}{2}$.

$\begin{array}{c}\frac{1}{2}\left(\overline{FC}\right)=\frac{1}{2}\left(\overline{SH}\right)\\ \overline{AC}=\overline{SA}\end{array}$

Step 3. State the conclusion.

Therefore, $\overline{AC}=\overline{SA}$ (proved).