Nila is constructing triangles for her math project. Choose ALL sets of line segment lengths that Nila can use
A 4 in, 6 in, 6 in
B 5 in, 5 in, 5 in
C 2 in, 2 in, 6 in
D 3 in, 4 in, 7 in
E 1 in, 2 in, 2 in
Nila can use sets A, B, and D to construct triangles as they satisfy the triangle inequality theorem where the sum of any two sides must be greater than the third side.
Set C and E do not satisfy this rule, as the sum of the two shorter sides in C is less than the longest side, and in E, the two shorter sides are equal but smaller than the longest side.
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To determine which sets of line segment lengths can be used to construct triangles, you need to apply the triangle inequality theorem. According to this 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 analyze each set of line segment lengths:
A: 4 in, 6 in, 6 in
The sum of the two shorter sides is 4 in + 6 in = 10 in, which is greater than the longest side of 6 in. Therefore, this set of line segment lengths can be used to construct a triangle.
B: 5 in, 5 in, 5 in
In this case, all three sides are equal in length. The sum of any two sides is 5 in + 5 in = 10 in, which is equal to the length of the third side. Therefore, this set of line segment lengths can also be used to construct a triangle.
C: 2 in, 2 in, 6 in
The sum of the two shorter sides is 2 in + 2 in = 4 in, which is less than the longest side of 6 in. According to the triangle inequality theorem, this set of line segment lengths cannot be used to construct a triangle.
D: 3 in, 4 in, 7 in
The sum of the two shorter sides is 3 in + 4 in = 7 in, which is equal to the length of the longest side. Therefore, this set of line segment lengths can be used to construct a triangle.
E: 1 in, 2 in, 2 in
The sum of the two shorter sides is 1 in + 2 in = 3 in, which is equal to the length of the longest side. Therefore, this set of line segment lengths can also be used to construct a triangle.
So, the sets of line segment lengths that Nila can use to construct triangles are:
A: 4 in, 6 in, 6 in
B: 5 in, 5 in, 5 in
D: 3 in, 4 in, 7 in
E: 1 in, 2 in, 2 in