Let's begin with recalling the Triangle Inequality Theorem. This theorem tells us that the sum of the lengths of any two sides in a triangle is greater than the length of the third side. Therefore, to determine if the given measures are correct we should add each pair of side lengths and check if it is greater than the third side length.
Sum of Two Lengths of Sides
The Third Side
An Inequality
22+ 23=45
45
45≯45
22+ 45=67
23
67>23
23+ 45=68
22
68>22
As we can see, the sum of the lengths of two shortest sides is not greater than the third side. Therefore, these measures are not correct.
