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

Question

which inequality explains why these three segments cannot be used to construct a triangle? ef + fd>de ed + efdf ef + fd

Accepted Answer

# Explanation:
## Step1: Recall triangle - inequality theorem
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
## Step2: Analyze each option
If $EF + FD<DE$, it violates the triangle - inequality theorem. In a triangle, if the sum of two side - lengths is less than the third side - length, the segments cannot form a triangle. Options A and C satisfy the triangle - inequality theorem, and option B has the wrong inequality sign for the sides $ED$, $EF$, and $DF$ in terms of the correct relationship for non - triangle formation.

# Answer:
D. $EF + FD<DE$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall triangle - inequality theorem

Step2: Analyze each option

Answer: