Question

which statements regarding △efg are true? select three options. ef + fg > eg eg + fg > ef eg - fg < ef ef - fg > eg eg + ef < fg

Explanation:

Step1: Apply triangle inequality theorem

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. So, for \(\triangle EFG\), \(EF + FG>EG\) (sum of two sides \(EF\) and \(FG\) is greater than the third side \(EG\)), \(EG + FG>EF\) (sum of two sides \(EG\) and \(FG\) is greater than the third side \(EF\)).

Step2: Derive from triangle inequality theorem

Also, from \(EF + FG>EG\), we can rewrite it as \(EF>EG - FG\) (by subtracting \(FG\) from both sides), which is equivalent to \(EG - FG

Answer:

EF + FG > EG, EG + FG > EF, EG - FG < EF