Answer:
1) Yes
2) Yes
3) Yes
4) No
5) Yes
6) Yes
7) Yes
8) Yes
9) Yes
10) No
Explanation:
The triangle inequality theorem states that the length of any 2 sides of a triangle must be greater than the third side of that same triangle.
1) By Inspection, 2 + 10 > 11.
Thus, this set can be lengths of the sides of a triangle
2) 7 + 9 > 10
Yes, this set can be lengths of the sides of a triangle
3) 11 + 7 > 12
Yes, this set can be lengths of the sides of a triangle
4) 11 + 7 < 20
No, this set cannot be lengths of the sides of a triangle
5) 10 + 8 > 13
Yes, this set can be lengths of the sides of a triangle
6) 7 + 2 > 7
Yes, this set can be lengths of the sides of a triangle
7) 5 + 12 > 13
Yes, this set can be lengths of the sides of a triangle
8) 13 + 12 > 18
Yes, this set can be lengths of the sides of a triangle
9) 11 + 3 > 13
Yes, this set can be lengths of the sides of a triangle
10) 12 + 3 < 19
No, this set cannot be lengths of the sides of a triangle