Tricks in the Hinge Theorem

Level 2 Problem ?

Question:

This is a triangle.  Mentally determine if this is a possible triangle.  It is not 180 degrees.

Solution:

Many people who have had a decent course in geometry should find this problem should not be included in the area of "hard math problems".  But then again, many people make mistakes.  Consider the triangle to have side lengths of a,b, and c .The Hinge Theorem states that in any triangle; a+b>c, b+c>a, a+c>b.  When two sides are added up the total should be greater that the third side.

However, in this problem a +b is not >c.  In fact a+b=c which tells us that this is not a possible triangle.  This tells us that this is not a triangle.

This is a good example of this theorem put into action.

Answer: not a triangle