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Q6

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 $\overline{EC}$, bisects $\overline{AF}$ .

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. State the conclusion.

As E is the midpoint of $\overline{AF}$, then any line passing through E also bisects $\overline{AF}$,

Since the line $\overline{EC}$ passes through the point E, then $\overline{EC}$ bisects $\overline{AF}$.

Therefore, the statement about the diagram is justified by the reason that the midpoint of a line divides it into equal parts.