Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle. (1 point)
• 9,4. 3
• 8, 1.7
• 2,7.6
• 12. 10, 22
To apply the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's examine each group of side measures:
1) 9, 4, 3
In this case, 9 + 4 is equal to 13, which is greater than 3. Also, 9 + 3 is equal to 12, which is greater than 4. Lastly, 4 + 3 is equal to 7, which is less than 9. Since the sum of the two smaller sides (4 and 3) is not greater than the longest side (9), this group of side measures will NOT form a triangle.
2) 8, 1.7
Here, 8 + 1.7 is equal to 9.7, which is greater than 1.7. Also, 8 + 1.7 is equal to 9.7, which is greater than 8. Lastly, 1.7 + 8 is equal to 9.7, which is greater than 1.7. Since the sum of the two smaller sides (1.7 and 8) is greater than the longest side (8), this group of side measures WILL form a triangle.
3) 2, 7.6
In this case, 2 + 7.6 is equal to 9.6, which is greater than 2. Also, 2 + 7.6 is equal to 9.6, which is greater than 7.6. Lastly, 7.6 + 2 is equal to 9.6, which is greater than 7.6. Since the sum of the two smaller sides (2 and 7.6) is greater than the longest side (7.6), this group of side measures WILL form a triangle.
4) 12, 10, 22
Here, 12 + 10 is equal to 22, which is equal to 22. Also, 12 + 22 is equal to 34, which is greater than 10. Lastly, 10 + 22 is equal to 32, which is greater than 12. Since the sum of the two smaller sides (10 and 22) is greater than the longest side (22), this group of side measures WILL form a triangle.
In summary, the groups of side measures that WILL form a triangle are:
- 8, 1.7
- 2, 7.6
- 12, 10, 22