Question

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
ED + EF > DF
EF + FD < DE

Answer 1

ED + EF < DF

(second option listed)

Explanation:

for a triangle, the sum of the two shorter side lengths must be greater than the larger side length

so we know that the two smaller lengths (DE and FE) would have to add up to be greater than the larger side length (DF)

because this is not the case, we know that we cannot construct a triangle

[to construct a triangle:]

smaller + smaller > bigger

DE + FE > DF; which is false/not the case

so because DE + FE < DF, we cannot form a triangle

so, ED + EF < DF explains why these three segments cannot construct a triangle

Answer 2

ED + EF < DF

Explanation:

shorter side lengths added together > larger side length

however, smaller side lengths are < larger

So ED + ED < DF means that this cannot be a triangle