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Elementary Geometry for College St...

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

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BuyFindarrow_forward

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 angles of a parallelogram are congruent.

To determine

To write:

A formal proof of the corollary, the opposite angles 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.

Description:

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 a
transversal, the alternate interior angles are congruent.
4. AD-BC- 4

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