Question

1. (02.04 mc)

in \\( \triangle efg \\), is it possible for \\( \overline{ge} \\) to measure 9 units? (2 points)
options:

• yes, because \\( 3 + 5 > 9 \\), \\( 5 + 9 > 3 \\), and \\( 9 + 3 > 5 \\)
• no, because \\( 3 + 5 > 9 \\), \\( 5 + 9 > 3 \\), and \\( 9 + 3 > 5 \\)
• yes, because \\( 3 + 5 > 9 \\), \\( 5 + 9 > 3 \\), and \\( 9 + 3 > 8 \\)
• no, because \\( 3 + 5 > 9 \\), \\( 5 + 9 > 3 \\), and \\( 9 + 3 > 5 \\)

Explanation:

Step1: Recall triangle inequality rule

For three lengths to form a triangle, the sum of any two sides must be greater than the third side.

Step2: Test the given side lengths

The sides would be 3, 5, 9.
Check $3+5 > 9$: $8 > 9$ → False
Check $5+9 > 3$: $14 > 3$ → True
Check $9+3 > 5$: $12 > 5$ → True

Answer:

No, because $3+6<9$, $6+9>3$, and $9+3>6$ (Note: correction to the option text logic: the actual invalid sum is $3+5=8<9$, which matches the core reasoning of this option)