Find the possiable measures for line segmant xy in triangle xyz if xz is 6 and yz is six. Im really confused- if you could explain this i would really appericate it! Thanks!
The possible values of the the length of one side of a triangle lie in a range between the sum and the difference of the other two.
In this case, that would be 0 < xy < 12
The length of two sides of the triangle must add up to a length longer than the third side. To determind this you add the two sides that you know, and the 3rd side is less than that (since 6+6 = 12, the third side must be LESS than 12) and you need to subtract those same two sides to find out the possible length again (since 6 - 6 = 0 the 3rd side must be greater than zero)
To find the possible measures for line segment XY in triangle XYZ, we can use the triangle inequality theorem. According to this theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we are given that XZ is 6 units long and YZ is also 6 units long. We want to find the possible measures for XY.
To apply the triangle inequality theorem, we need to consider all the possible combinations of side lengths. Let's explore the different cases:
1) XZ + YZ > XY:
Substituting the given values, we have 6 + 6 > XY.
Simplifying the expression, we get 12 > XY.
2) XZ + XY > YZ:
Substituting the given values, we have 6 + XY > 6.
Simplifying the expression, we get XY > 0 (since we cannot have a negative length).
3) YZ + XY > XZ:
Substituting the given values, we have 6 + XY > 6.
Simplifying the expression, we get XY > 0 (since we cannot have a negative length).
From the above cases, we can conclude that XY must be greater than 0 and less than 12 (i.e., 0 < XY < 12). This means that any value of XY within this range would satisfy the triangle inequality theorem.
Thus, the possible measures for line segment XY in triangle XYZ are any real numbers between 0 and 12.