Chapter 5.4, Problem 34E

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

Elementary Geometry For College St...

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

Given: Δ A B C is not a right Δ Prove: a 2 + b 2 ≠ c 2 (Note: AB = c, AC = b and CB = a.)

To determine

To Proof :

c2a2+b2.

Explanation

Given:

Î”ABC is not a right Î”

AB=c, AC=b and CB=a.

Approach:

Now a, b and c are the lengths of the three sides of the triangle, with c is the longest side, then

From the triangle theorems,

1. If the square of the length of the longest side is greater than the sum of square of the lengths of other two sides then the triangle is Obtuse.

c2>a2+b2

2. If the square of the length of the longest side is less than the sum of square of the lengths of other two sides then the triangle is Acute.

c2<a2+b2

3. If the square of the length of the longest side is equal to the sum of square of the lengths of other two sides then the triangle is Right triangle.

c2=a2+b2.

So given ABC is not a right triangle then the triangle must be Obtuse or Acute triangle

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