Question

In triangle EFG, where segment EF measures 3 units and segment FG measures 5 units, is it possible for segment GE to measure 6 units?

1) Yes, because 3 + 5 > 6, 5 + 6 > 3, and 6 + 3 > 5
2) No, because 3 + 5 > 6, 5 + 6 > 3, and 6 + 3 > 5
3) Yes, because 3 + 5 < 6, 5 + 6 < 3, and 6 + 3 < 5
4) No, because 3 + 5 < 6, 5 + 6 < 3, and 6 + 3 < 5

Answer 1

In triangle EFG, it is not possible for segment GE to measure 6 units because it violates the condition that the sum of any two sides must be greater than the third side.

Step-by-step explanation:

In triangle EFG, where segment EF measures 3 units and segment FG measures 5 units, it is not possible for segment GE to measure 6 units. The sum of any two sides of a triangle must be greater than the third side for the triangle to be valid. In this case, 3 + 5 is equal to 8, which is greater than 6. However, for segment GE to measure 6 units, it would violate the condition that the sum of any two sides must be greater than the third side.

Therefore, the correct answer is No, because 3 + 5 > 6, 5 + 6 > 3, and 6 + 3 > 5.