To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Let's check each group of side measures:
A) 2, 7, 6
2 + 7 = 9 > 6
2 + 6 = 8 > 7
6 + 7 = 13 > 2
All the sums of any two sides are greater than the third side. Therefore, the side measures 2, 7, and 6 can form a triangle.
B) 9, 4, 3
9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9
Similarly, all the sums of any two sides are greater than the third side. Therefore, the side measures 9, 4, and 3 can form a triangle.
C) 12, 10, 22
12 + 10 = 22 = 22 (sum of two sides equal to the third side)
In this case, the sum of the side measures 12 and 10 is equal to the third side measure 22. According to the Triangle Inequality Theorem, the sums of any two sides should be greater than the third side. Since this condition is not met, the side measures 12, 10, and 22 cannot form a triangle.
D) 8, 1, 7
8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 > 8
As before, all the sums of any two sides are greater than the third side. Therefore, the side measures 8, 1, and 7 can form a triangle.
In summary, groups A, B, and D form triangles while group C does not.
Apply the Triangle Inequality Theorem and determine which group of side measures will for a triangle.
A) 2, 7, 6
B) 9, 4, 3
C) 12, 10, 22
D) 8, 1, 7
3 answers
there is only one answer
Apologies for the mistake. I made a miscalculation in my previous response.
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 third side.
Let's recheck each group of side measures:
A) 2, 7, 6
2 + 7 = 9 > 6
2 + 6 = 8 > 7
6 + 7 = 13 > 2
All the sums of any two sides are greater than the third side. Therefore, the side measures 2, 7, and 6 can form a triangle.
B) 9, 4, 3
9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9
Similarly, all the sums of any two sides are greater than the third side. Therefore, the side measures 9, 4, and 3 can form a triangle.
C) 12, 10, 22
12 + 10 = 22 > 22 (sum of two sides not greater than the third side)
12 + 22 = 34 > 10
10 + 22 = 32 > 12
In this case, the sum of the side measures 12 and 10 is not greater than the third side measure 22. According to the Triangle Inequality Theorem, the sums of any two sides should be greater than the third side. Since this condition is not met, the side measures 12, 10, and 22 cannot form a triangle.
D) 8, 1, 7
8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 > 8
As before, all the sums of any two sides are greater than the third side. Therefore, the side measures 8, 1, and 7 can form a triangle.
In summary, groups A and B can form triangles, while groups C and D cannot.
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 third side.
Let's recheck each group of side measures:
A) 2, 7, 6
2 + 7 = 9 > 6
2 + 6 = 8 > 7
6 + 7 = 13 > 2
All the sums of any two sides are greater than the third side. Therefore, the side measures 2, 7, and 6 can form a triangle.
B) 9, 4, 3
9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9
Similarly, all the sums of any two sides are greater than the third side. Therefore, the side measures 9, 4, and 3 can form a triangle.
C) 12, 10, 22
12 + 10 = 22 > 22 (sum of two sides not greater than the third side)
12 + 22 = 34 > 10
10 + 22 = 32 > 12
In this case, the sum of the side measures 12 and 10 is not greater than the third side measure 22. According to the Triangle Inequality Theorem, the sums of any two sides should be greater than the third side. Since this condition is not met, the side measures 12, 10, and 22 cannot form a triangle.
D) 8, 1, 7
8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 > 8
As before, all the sums of any two sides are greater than the third side. Therefore, the side measures 8, 1, and 7 can form a triangle.
In summary, groups A and B can form triangles, while groups C and D cannot.
1 answer