Chapter 4.1, Problem 2MRE

To determine

To prove: $\overline{SA}=\overline{AC}$

Explanation of Solution

Given information: $\overline{FC},\overline{SH}$ bisect each other at $A$ and $\overline{FC}=\overline{SH}$

Proof:

  

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

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

Also,

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

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

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

Hence proved.