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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 :

sqdancefan

Answer:

  (b)  ED + EF < DF

Step-by-step explanation:

You want to know why DE = 1/2DF, FE = 1/3DF, and DF cannot be used to form a triangle.

Triangle inequality

The triangle inequality requires the sum of the two short sides of a triangle exceed the length of the long side. Here, that would require ...

  ED + EF > DF

However, we have ...

  (1/2)DF + (1/3)DF = (5/6)DF < DF

The short sides total a length less than DF, so cannot be used to form a triangle.

  ED +EF < DF . . . . . choice B

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