Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
2, 7, 6
12, 10, 22
9, 4, 3
8, 1, 7
AAAaannndd the bot gets it wrong yet again!
only the 1st
To determine if a set of side lengths can form a triangle, we need to apply the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply the Triangle Inequality Theorem to the given sets of side measures:
1. For the set of side measures 2, 7, 6:
- Checking each pair of sides, we have:
- 2 + 7 = 9 > 6
- 2 + 6 = 8 > 7
- 7 + 6 = 13 > 2
All three sums fulfill the condition, so the side measures 2, 7, and 6 can form a triangle.
2. For the set of side measures 12, 10, 22:
- Checking each pair of sides, we have:
- 12 + 10 = 22 > 22
- 12 + 22 = 34 > 10
- 10 + 22 = 32 > 12
The first sum of the side measures does not satisfy the condition. Therefore, the side measures 12, 10, and 22 cannot form a triangle.
3. For the set of side measures 9, 4, 3:
- Checking each pair of sides, we have:
- 9 + 4 = 13 > 3
- 9 + 3 = 12 > 4
- 4 + 3 = 7 > 9
The third sum of the side measures does not satisfy the condition. Hence, the side measures 9, 4, and 3 cannot form a triangle.
4. For the set of side measures 8, 1, 7:
- Checking each pair of sides, we have:
- 8 + 1 = 9 > 7
- 8 + 7 = 15 > 1
- 1 + 7 = 8 > 8
The third sum of the side measures does not satisfy the condition. Therefore, the side measures 8, 1, and 7 cannot form a triangle.
To summarize, the group of side measures that can form a triangle is 2, 7, and 6.
To determine whether a set of side measures can form a triangle, we need to apply the Triangle Inequality Theorem. According to this theorem, the sum of any two side lengths of a triangle must be greater than the third side length.
Let's go through each group of side measures to determine if they can form a triangle or not:
1. 2, 7, 6
For this group, we need to check if the sum of any two sides is greater than the third side.
- 2 + 7 = 9, which is greater than 6.
- 2 + 6 = 8, which is greater than 7.
- 7 + 6 = 13, which is also greater than 2.
Since the sum of any two sides is greater than the third side for all combinations, the side measures 2, 7, and 6 can form a triangle.
2. 12, 10, 22
Let's check the sums of the side measures:
- 12 + 10 = 22, which is equal to 22. This is not greater than 22.
- 12 + 22 = 34, which is greater than 10.
- 10 + 22 = 32, which is greater than 12.
Since the sum of one of the side measures is not greater than the third side for at least one combination, the side measures 12, 10, and 22 cannot form a triangle.
3. 9, 4, 3
Checking the sums of the side measures:
- 9 + 4 = 13, which is greater than 3.
- 9 + 3 = 12, which is greater than 4.
- 4 + 3 = 7, which is less than 9.
Similar to the previous case, the sum of 4 and 3 is not greater than 9, so the side measures 9, 4, and 3 cannot form a triangle.
4. 8, 1, 7
Let's check the sums of the side measures:
- 8 + 1 = 9, which is greater than 7.
- 8 + 7 = 15, which is greater than 1.
- 1 + 7 = 8, which is greater than 8.
In this case, the sum of any two side measures is greater than the third side, so the side measures 8, 1, and 7 can form a triangle.
In conclusion, the group of side measures that can form a triangle is:
2, 7, 6
and
8, 1, 7