Question

Triangle E F G is shown.
Which statements regarding Triangle E F G are true? Select three options.

E F + F G greater-than E G
E G + F G greater-than E F
E G minus F G less-than E F
E F minus F G greater-than E G
E G + E F less-than F G

Answer 1

True are the first three:

- EF + FG > EG (sum of any two sides > the third)
- EG + FG > EF (same)
- EG − FG < EF (rearrange EF + FG > EG → EG − FG < EF)

The last two are false (EF − FG > EG contradicts EF < EG + FG, and EG + EF < FG contradicts the triangle inequality).