   Chapter 4.2, Problem 25E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 25 to 28, write a formal proof of each theorem or corollary.If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

To determine

To write:

A formal proof of the theorem ‘if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram’.

Explanation

Formal proof,

Statement:

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Drawing:

Given:

ABCD is a quadrilateral

AB¯CD¯,

Prove:

ABCD is a parallelogram

Calculation:

 PROOF Statement Reason 1 ABCD is a quadrilateral,AB¯≅CD¯,AD¯≅BC¯ 1

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