Question

Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)

Responses

12, 10, 22
12, 10, 22

9, 4, 3
9, 4, 3

8, 1, 7
8, 1, 7

2, 7, 6

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if a group of side measures will form a triangle, we need to apply the Triangle Inequality Theorem. According to the theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's apply the theorem to the given groups of side measures:

1) 12, 10, 22:
12 + 10 = 22 > 22 (True)
12 + 22 = 34 > 10 (True)
10 + 22 = 32 > 12 (True)

All the sums of the side lengths are greater than the length of the remaining side, so this group of side measures will form a triangle.

2) 9, 4, 3:
9 + 4 = 13 > 3 (True)
9 + 3 = 12 > 4 (True)
4 + 3 = 7 > 9 (False)

The sum of the side lengths 4 + 3 is not greater than the length of the remaining side 9. Therefore, this group of side measures will not form a triangle.

3) 8, 1, 7:
8 + 1 = 9 > 7 (True)
8 + 7 = 15 > 1 (True)
1 + 7 = 8 > 8 (False)

The sum of the side lengths 1 + 7 is not greater than the length of the remaining side 8. Therefore, this group of side measures will not form a triangle.

4) 2, 7, 6:
2 + 7 = 9 > 6 (True)
2 + 6 = 8 > 7 (True)
7 + 6 = 13 > 2 (True)

All the sums of the side lengths are greater than the length of the remaining side, so this group of side measures will form a triangle.

Based on the Triangle Inequality Theorem, the groups of side measures that will form a triangle are:

1) 12, 10, 22
4) 2, 7, 6

Answer 2

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