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To determine if it is possible for side \( \overline{GE} \) to measure 6 units in triangle \( \Delta EFG \), we need to apply the **Triangle Inequality Theorem**. This 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.

We are given:
- \( \overline{EF} = 3 \) units
- \( \overline{FG} = 5 \) units
- We want to check if \( \overline{GE} \) can be 6 units.

### Step 1: Check Triangle Inequality
We need to verify three conditions:
1. \( \overline{EF} + \overline{FG} > \overline{GE} \)  
   \( 3 + 5 = 8 > 6 \) (This is true.)
   
2. \( \overline{EF} + \overline{GE} > \overline{FG} \)  
   \( 3 + 6 = 9 > 5 \) (This is true.)
   
3. \( \overline{FG} + \overline{GE} > \overline{EF} \)  
   \( 5 + 6 = 11 > 3 \) (This is true.)

### Conclusion:
Since all three inequalities are satisfied, it is indeed **possible** for \( \overline{GE} \) to measure 6 units.

The correct answer is:
- **Yes, because \( 3 + 5 > 6 \), \( 5 + 6 > 3 \), and \( 6 + 3 > 5 \).**

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How would the result change if \( \overline{GE} \) were 7 units instead of 6?
2. Can you apply the Triangle Inequality Theorem to any triangle in general?
3. What is the significance of the Triangle Inequality Theorem in determining if three given lengths can form a triangle?
4. How can you determine the type of triangle (acute, obtuse, right) using side lengths?
5. What happens to the Triangle Inequality Theorem in the case of a degenerate triangle?

**Tip:** The Triangle Inequality Theorem is a fundamental property to check if a given set of side lengths can actually form a valid triangle!

In ΔEFG, is it possible for GE to measure 6 units?

Explore whether side GE in triangle ΔEFG can measure 6 units using the Triangle Inequality Theorem. Learn about the key conditions to check for valid triangle side lengths. Suitable for students in Grades 6-8.

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