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Q6

Expert-verified

Geometry

Found in: Page 45

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

State which postulate, definition, or theorem justifies the statement about the diagram.
If E is the midpoint of $\bar{A F}$ , then $\bar{E C}$ , bisects $\bar{A F}$ .

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 by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $\bar{A F}$ , then any line passing through E also bisects $\bar{A F}$ ,

Since the line $\bar{E C}$ passes through the point E, then $\bar{E C}$ bisects $\bar{A F}$ .

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

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