Question

which inequality explains why these three segments cannot be used to construct a triangle?\
\\( \bigcirc \\) \\( ef + fd > de \\)\
\\( \bigcirc \\) \\( ed + ef < df \\)\
\\( \bigcirc \\) \\( ed + ef > df \\)\
\\( \bigcirc \\) \\( ef + fd < de \\)

Explanation:

Step1: Recall triangle inequality theorem

The sum of any two sides must be greater than the third side for a triangle to exist. If the sum of two sides is less than or equal to the third, no triangle can form.

Step2: Analyze the options

Check which option violates the theorem:

• $EF + FD > DE$: Satisfies the theorem (sum > third side).
• $ED + EF < DF$: Violates the theorem (sum < third side).
• $ED + EF > DF$: Satisfies the theorem.
• $EF + FD < DE$: Violates, but the figure shows $DF$ is the longest segment (since $D$ and $F$ are endpoints of the longest line), so $ED + EF$ should relate to $DF$. The correct violation is $ED + EF < DF$.

Answer:

B. ED + EF < DF