# Triangle innequality proof question

• transgalactic
In summary, the conversation discusses using the triangle inequality to prove a statement involving real numbers a and b. The inequality states that the absolute value of the sum of two numbers is less than or equal to the sum of the absolute values of the individual numbers. To apply it to the given question, the participants suggest using specific values for x and y, and utilizing the fact that the absolute value of a difference is equal to the absolute value of the negative of that difference. A variable c is also mentioned as a threshold for determining the magnitude of |a-b|.
transgalactic
for "a" and "b" are real numbers prove that:

http://img352.imageshack.us/my.php?image=34860604zw7.gif

i need to use the triangle innequality
|a|-|b|=< |a+b| <= |a| + |b|

how to apply it to my question?
it a long way from
triangle innequality formula to the expression that i was given in the question

??

|x+y|<=|x|+|y|
or
|x|>=|x+y|-|y|

for any two vectors x,y

Take in particular

x=a-b, y=b

and

x=b-a, y=a

What do you get?
Then use, |a-b|=|b-a| and the fact that if |a-b| is greater than c and greater then -c, it must be greater than |c|. (What is c?)

## 1. How do I prove the triangle inequality?

To prove the triangle inequality, you must show that the sum of any two sides of a triangle is greater than the length of the third side.

## 2. What is the triangle inequality theorem?

The triangle inequality theorem states that the sum of any two sides of a triangle is always greater than the length of the third side.

## 3. What is the importance of the triangle inequality?

The triangle inequality is important because it helps us determine if a set of three lengths can form a triangle. It also plays a crucial role in many geometric proofs and theorems.

## 4. What are the different ways to prove the triangle inequality?

There are several ways to prove the triangle inequality, including using the Pythagorean theorem, the Law of Cosines, or the Triangle Sum Theorem.

## 5. Can the triangle inequality be applied to all triangles?

Yes, the triangle inequality applies to all triangles, regardless of their shape or size.

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