apply the triangle inequality theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. list them in ascending order least to greatest.
the measures of the third side could be blank blank or blank
9
2
3
8
6
5
4
10
7
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the first two sides measure 6 and 2.
We can apply the triangle inequality theorem to determine the possible whole number measures of the third side:
6 + 2 > third side
8 > third side
So, the possible whole number measures of the third side are any numbers that are greater than 8.
Listing them in ascending order from least to greatest:
9
10
must pick three answers
Apologies for the confusion. Let's apply the triangle inequality theorem again:
6 + 2 > third side
8 > third side
Therefore, the possible whole number measures of the third side are any numbers that are greater than 8.
Listing them in ascending order from least to greatest:
9
10
identify the side measures that will not form a triangle
2 2 1
3 3 6
3 3 4
2 2 2
To determine if the given side measures will form a triangle, we 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.
Let's analyze each set of side measures:
1) 2, 2, 1:
The sum of the two smaller sides is 2 + 1 = 3, which is not greater than the length of the remaining side (2).
Therefore, the measures 2, 2, 1 will not form a triangle.
2) 3, 3, 6:
The sum of the two smaller sides is 3 + 3 = 6, which is equal to the length of the remaining side (6).
Therefore, the measures 3, 3, 6 will not form a triangle.
3) 3, 3, 4:
The sum of the two smaller sides is 3 + 3 = 6, which is greater than the length of the remaining side (4).
Therefore, the measures 3, 3, 4 will form a triangle.
4) 2, 2, 2:
The sum of the two smaller sides is 2 + 2 = 4, which is equal to the length of the remaining side (2).
Therefore, the measures 2, 2, 2 will form a triangle.
So, the side measures that will not form a triangle are:
- 2, 2, 1
- 3, 3, 6
pick either 2 2 1 or 3 3 6
I apologize for the confusion caused by my previous response.
The side measures 3, 3, 6 will not form a triangle. According to 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. In this case, 3 + 3 = 6, which is equal to the length of the remaining side. Therefore, a triangle cannot be formed with side measures 3, 3, 6.
sort into categories unique triangles not unique triangles many triangles and no trianglles impossible
8m 1m 8m
30 70 80
90 40 40
10cm 12cm 22cm
must pick three
Sure, let's categorize these triangles:
Unique Triangles:
1) 8m 1m 8m
2) 10cm 12cm 22cm
Not Unique Triangles:
3) 30 70 80
Many Triangles (Degenerate Triangles):
- None of the given sets of side measures fall into this category as they do not form a line segment.
No Triangles Impossible Case:
- None of the given sets of side measures fall into this category as they all have the potential to form triangles.