Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
(1 point)
O 12, 10. 22
O 9. 4. 3
O 2,7,6
O 8, 1, 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.
Let's apply this theorem to the given groups of side measures:
1) For the first set of side measures (12, 10, 22):
- 12 + 10 = 22 (greater than 22) ✓
- 10 + 22 = 32 (greater than 12) ✓
- 12 + 22 = 34 (greater than 10) ✓
Since the sum of the lengths of any two sides is greater than the length of the third side, this set of side measures will form a triangle.
2) For the second set of side measures (9, 4, 3):
- 9 + 4 = 13 (greater than 3) ✓
- 4 + 3 = 7 (less than 9) ✗
- 9 + 3 = 12 (greater than 4) ✓
This set of side measures will not form a triangle.
3) For the third set of side measures (2, 7, 6):
- 2 + 7 = 9 (greater than 6) ✓
- 7 + 6 = 13 (greater than 2) ✓
- 2 + 6 = 8 (greater than 7) ✓
This set of side measures will form a triangle.
4) For the fourth set of side measures (8, 1, 7):
- 8 + 1 = 9 (greater than 7) ✓
- 1 + 7 = 8 (less than 8) ✗
- 8 + 7 = 15 (greater than 1) ✓
This set of side measures will not form a triangle.
In conclusion, the groups of side measures that will form a triangle are:
- 12, 10, 22
- 2, 7, 6