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prove that for any real values of x,y
| |x|-|y| | <= |x+y| <= |x| + |y|
| |x|-|y| | <= |x+y| <= |x| + |y|
| |x|-|y| | <= a
then
|x|-|y| <= a
which gives
|x|-|y| <= |x+y| <= |x|+|y|
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the third side.
You can use the Triangle Inequality Theorem to determine if a set of three side lengths can form a triangle. If the sum of any two sides is greater than the third side, then a triangle can be formed. You can also use it to find the range of possible values for a missing side length.
Yes, the Triangle Inequality Theorem does not apply to degenerate triangles, which are triangles with all three points lying on the same line. In these cases, the sum of any two sides will be equal to the third side.
No, the Triangle Inequality Theorem only applies to triangles. It is a specific property of triangles and cannot be applied to other shapes.
The Pythagorean Theorem is a special case of the Triangle Inequality Theorem. When the triangle is a right triangle, the Pythagorean Theorem can be used to determine the length of the third side, while the Triangle Inequality Theorem can be used to determine if a triangle can be formed with the given side lengths.