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: Recall triangle inequality theorem

In a triangle, the sum of the lengths of any two sides is greater than the length of the third side. So for \(\triangle EFG\), \(EF + FG>EG\), \(EG + FG>EF\), \(EF + EG>FG\). Also, the difference of the lengths of any two sides is less than the length of the third side. So \(|EF - FG|

Step2: Analyze each option

• For \(EF + FG>EG\): This satisfies the triangle - inequality theorem.
• For \(EG + FG>EF\): This satisfies the triangle - inequality theorem.
• For \(EG - FG
• For \(EF - FG>EG\): This violates the triangle - inequality theorem (because \(EF - FG
• For \(EG + EFFG\)).

Answer:

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