   Chapter 1.7, Problem 32E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 27 to 35, complete the formal proof of each theorem.If two line segments are congruent, then their midpoints separate these segments into four congruent segments. Given: A B ¯ ≅ D C ¯ M is midpoint of A B ¯ N is midpoint of D C ¯ Prove: A M ¯ ≅ M B ¯ ≅ D N ¯ ≅ N C ¯ To determine

To find:

The complete formal proof of the given theorem.

If two line segments are congruent, then their midpoints separate these segments into four congruent segments.

Explanation

Given:

The statement of given theorem is,

If two line segments are congruent, then their midpoints separate these segments into four congruent segments.

Given: AB¯DC¯, M is midpoint of AB¯ and N is midpoint of DC¯

Prove: AM¯MB¯DN¯NC¯

The given figure is,

Approach:

The formal proof of given theorem is shown in the following table.

 Statements Reasons 1. M is midpoint of AB¯ and N is midpoint of DC¯ 1. Given 2. AM¯≅MB¯ and DN¯≅NC¯ 2. If a midpoint separates the line segment into two parts, then two parts are congruent. 3. AM=MB and DN=NC 3. The length of two congruent line segments is same. 4. AB=AM+MB and DC=DN+NC 4

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