   Chapter 4.1, 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 31 to 34, write a formal proof of each theorem or corollary.The opposite sides of a parallelogram are congruent.

To determine

To write:

A formal proof of the corollary, the opposite sides of a parallelogram are congruent.

Explanation

Given:

A parallelogram with one diagonal.

Corollary:

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

Let the parallelogram be ABCD with the diagonal AC-.

 PROOF Statements Reasons 1. Parallelogram ABCD 1. Given 2. AB-∥DC- 2. By the definition of a parallelogram 3. ∠1=∠2 3. If two ∥ lines are cut by atransversal, the alternate interior ∠s are congruent. 4. AD-∥BC- 4. Same as reason 2 5. ∠3=∠4 5

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