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 two sides > third)
- EG + FG > EF (sum of two sides > third)
- EG − FG < EF (equivalently |EG − FG| < EF, the difference of two sides is less than the third)

The last two are false (they contradict the triangle inequalities).