Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole

Chapter 1 - Section 1.5 - Introduction to Geometric Proof - Exercises - Page 45: 28

Answer

1. Given 2. The midpoint of a segment is equidistant from the two ends of the segment. 3. Segment-Addition Postulate 4. Substitution Property of Equality 5. Substitution or Distribution Property of Equality 6. Division Property of Equality

Work Step by Step

1. Given 2. The midpoint of a segment is equidistant from the two ends of the segment. 3. The sum of the two pieces ($\overline{DE}, \overline{EF}$) equals to $\overline{DF}$ 4. We can replace $\overline{EF}$ with $\overline{DE}$ because thy are egal. 5. DE + DE = $2\times DE$ 6. We divide the equality by 2 to prove the statement.

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