Question

Triangle efg in which segment ef measures 3 units and segment fg measures 5 units in δefg, is it possible for segment ge to measure 6 units? yes, because 3 5 > 6, 5 6 > 3, and 6 3 > 5 no, because 3 5 > 6, 5 6 > 3, and 6 3 > 5 yes, because 3 5 < 6, 5 6 < 3, and 6 3 < 5 no, because 3 5 < 6, 5 6 < 3, and 6 3 < 5

Answer 1

Yes, it is possible for a triangle to have sides measuring 3 units, 5 units, and 6 units as all conditions of the Triangle Inequality Theorem are satisfied.

Step-by-step explanation:

The question asks if it is possible for a triangle to have sides of length 3 units, 5 units, and 6 units. To determine this, we use the Triangle Inequality Theorem, which states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. For triangle EFG, the sides are EF (3 units), FG (5 units), and GE (6 units).

• EF + FG > GE: 3 + 5 > 6 or 8 > 6 is true.
• FG + GE > EF: 5 + 6 > 3 or 11 > 3 is true.
• GE + EF > FG: 6 + 3 > 5 or 9 > 5 is true.

All three conditions of the Triangle Inequality Theorem are satisfied, which means it is possible for a triangle to have sides of the given lengths. Therefore, yes, it is possible for segment GE to measure 6 units.