Can the sides of a triangle have lengths 2, 8, and 9? Choices: (A)yes (B)no

Triangle Inequality Theorem: To determine if these can be the sides of a triangle, we need to check 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. Check 2 + 8 > 9: Check if 2 + 8 > 9. Calculation: 2 + 8 = 10, and 10 > 9, so this part is true. Check 2 + 9 > 8: Check if 2 + 9 > 8. Calculation: 2 + 9 = 11, and 11 > 8, so this part is true. Check 8 + 9 > 2: Check if 8 + 9 > 2. Calculation: 8 + 9 = 17, and 17 > 2, so this part is true.

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Can the sides of a triangle have lengths $2$ , $8$ , and $9$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Q. Can the sides of a triangle have lengths

2

8

, and

9

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Triangle Inequality Theorem: To determine if these can be the sides of a triangle, we need to check 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.
Check 2 + 8 > 9: Check if 2 + 8 > 9. Calculation: $2 + 8 = 10$ , and 10 > 9, so this part is true.
Check 2 + 9 > 8: Check if 2 + 9 > 8. Calculation: $2 + 9 = 11$ , and 11 > 8, so this part is true.
Check 8 + 9 > 2: Check if 8 + 9 > 2. Calculation: $8 + 9 = 17$ , and 17 > 2, so this part is true.