   Chapter 4.2, Problem 26E 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 the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

To determine

To write:

A formal proof of the theorem ‘If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram”.

Explanation

Formal proof,

Statement:

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Drawing:

Given:

ABCD is a quadrilateral with diagonals AC and BD which bisect at ‘O’..

OA¯OC¯

OB¯OD¯.

Prove:

ABCD is a parallelogram.

 PROOF Statements Reasons 1. ABCD is a quadrilateral with diagonals AC and BD which intersect at; O’.OA¯≅OC¯OB¯≅OD¯ 1. Given 2. m∠BOA=m∠COD 2

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