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Expert-verified Found in: Page 45 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # State which postulate, definition, or theorem justifies the statement about the diagram. If E is the midpoint of $\overline{AF}$, then $AE=\frac{1}{2}AF$.

The fact that the midpoint of a line divides it into equal parts justifies the statement about the diagram.

See the step by step solution

## Step 1. Observe the given diagram. The diagram constitutes a straight-line AEF and two other lines meet the line AEF at the point E. E is the midpoint of AF.

## Step 2. State the midpoint theorem.

The theorem states that if E is the midpoint of AF, then AE is equal to EF.

## Step 3. Prove the statement.

As E is the midpoint of AF,

Then, $AE=EF$.

Also,

$\begin{array}{c}AE+EF=AF\\ AE+AE=AF\end{array}$

$2AE=AF$

$AE=\frac{1}{2}AF$

Hence, the statement is proved if the midpoint of a line divides it into equal parts.

Therefore, the statement about the diagram is justified by the reason that the midpoint of a line divides it into equal parts. ### Want to see more solutions like these? 