The sum of the lengths of any two sides of a triangle must be greater than the third side.
Provide the best answer* in the boxes below
If you have two sides of a triangle, say 10 inches and 12 inches, then it is IMPOSSIBLE for the third side to be more than 22 inches. It's IMPOSSIBLE because if you connect the two short sides and bend them in an angle, connecting the two remaining endpoints will be a line that is less than their sum (22 inches). If the third side is 22 inches it means that the other two sides are actually stretched out in a straight line in order to connect the two ends of the 22 inch side. So you see, the third side MUST be less than the sum of the other two sides. (or, as stated in our theorem, the sum of two sides must be greater than the length of the third).
*The best answer: "A triangle has sides that measure 10 and 12. The third side must be shorter than what length?" While 23, 24, 25, 26,... are all correct answers. They are not the best answers. If you answer 25, then it means that 24 might form a triangle with 10 and 12 - which it cannot. There for 22 is the BEST answer.