   Chapter 4.3, Problem 34E 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 34 to 39, write a formal proof of each theorem.The diagonals of a square are perpendicular.

To determine

To write:

A formal proof of the given theorem.

Explanation

Calculation:

Given: The diagonals of a square are perpendicular.

The diagonals of a rhombus are always perpendicular to each other, and a square is essentially a rhombus.

Consider ABCD is a square.

O is the point of intersection of AC and BD.

R.T.P: AOB=BOC=COD=AOD=90

Proof:

In AOB and BOC,

AB = BC (ABCD is a square)

OA = OC (Each diagonal of a parallelogram bisects the other)

OB = OB (Common)

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