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Q2

Expert-verified
Found in: Page 121

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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

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

See the 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).