Question

In ΔEFG, is it possible for segment GE to measure 4 units?

A. No, because 3 + 5 > 4, 5 + 4 > 3, and 4 + 3 > 5

B. Yes, because 3 + 5 4, 5 + 4 > 3, and 4 + 3 > 5

Answer 1

Yes, because 3 + 5 > 4, 5 + 4 > 3,

Explanation:

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, in the case of ΔEFG:

3 + 5 = 8, which is greater than 4

5 + 4 = 9, which is greater than 3

4 + 3 = 7, which is greater than 5

Therefore, the correct statement is: "Yes, because 3 + 5 > 4, 5 + 4 > 3, and 4 + 3 > 5." It is possible for segment GE to measure 4 units and form a valid triangle with segments EF and FG.

Answer 2

Substitution

Explanation:

We essentially have x = 180 and a+b+c = x.

So we are just substituting x for a+b+c