3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F. Which inequality explains why these three segments cannot be used to construct a triangle? EF + FD > DE ED + EF DF EF + FD < DE

The triangle inequality states that the sum of the two shortest side lengths must be greater than the largest side length of the triangle. Basically, we need to find if DE + FE > DF. We know that DE = 1/2 DF and FE = 1/3 DF so the inequality becomes 1/2 DF + 1/3 DF > DF which simplifies to 5/6 DF > DF. Since 5/6th of a number will never be greater than itself, the answer is ED + EF < DF.