   Chapter 5.6, Problem 31E 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

Complete the proof of this property:If a b = c d , then a + c b + d = a b and a + c b + d = c d PROOF Statements Reasons 1. a b = c d 1. ? 2. b ⋅ c = a ⋅ d 2. ? 3. a b + b c = a b + a d 3. ? 4. b ( a + c ) = a ( b + d ) 4. ? 5. a + c b + d = a b 5. Means-Extremes Property (symmetric form) 6. a + c b + d = c d 6. ?

To determine

To complete:

The proof of the property “If ab=cd, then a+cb+d=ab and a+cb+d=cd”.

Explanation

Given:

 Proof 1. ab=cd 1. ? 2. b⋅c=a⋅d 2.? 3. ab+bc=ab+ad 3.? 4. b(a+c)=a(b+d) 4.? 5. a+cb+d=ab 5.Means-Extremes Property (Symmetric form) 6. a+cb+d=cd 6. ?

Property used:

Means-Extremes Property:

In a proportion, the product of the means equals the product of the extremes; that is, if ab=cd (where b0 and d0), then ad=bc.

Alternative forms of proportions:

In a proportion, the means or the extremes (or both) may be interchanged; that is, if ab=cd (where a, b, c, and d are nonzero), then ac=bd, db=ca and dc=ba.

Calculation:

Given: ab=cd

By means-extremes property, we get bc=ad

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