Can each set line segments form a triangle? Why or why not?
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AB = 1/2 mile
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BC = 1/3 mile
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AC = 1/4 mile
Please help. Thank you
1/2 = 6/12
1/3 = 4/12
1/4 = 3/12
the longest side is not longer than the sum of the two shorter sides , so a triangle can be made
To determine whether a set of line segments 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 this theorem to the given set of line segments:
AB = 1/2 mile
BC = 1/3 mile
AC = 1/4 mile
To check if these segments can form a triangle, we need to consider all possible combinations of two sides and compare their sum with the length of the remaining side.
1. AB + BC > AC:
1/2 + 1/3 > 1/4
5/6 > 1/4
2. AB + AC > BC:
1/2 + 1/4 > 1/3
3/4 > 1/3
3. BC + AC > AB:
1/3 + 1/4 > 1/2
7/12 > 1/2
From the above calculations, we can see that all three conditions are satisfied. Therefore, the given set of line segments (AB, BC, and AC) can form a triangle.
In summary, to determine if a set of line segments can form a triangle, you need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Compare the sum of all possible combinations of two sides with the length of the remaining side. If all three conditions are satisfied, then the line segments can form a triangle.
AB
1/4
mile 4.
DE 0.205 kilometer
BC
1/3
mile
EF 0.01 kilometer
AC
1/4
mile
Draw out a comparable triangle, using parts of a foot instead of a mile.
A squared plus B squared equals C squared. C being the hypotenuse (longest side)
Find out which sides arn't the hypotenuse, then square them, add them, and see if they make up the third side :)
If it was me I would get rid of the fractions and put it into decimals too....