Can each set of line segments form a triangle? why or why not?
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De =0.205 kilometer
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Ef = 0.01 kilometer
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Df =0.02 kilometer
This question makes no sense.
DE is the longest, so you need
EF+DF > DE
To determine whether each set of line segments can form a triangle, we need to apply the triangle inequality theorem. According to this 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 check:
1. De = 0.205 kilometer, Ef = 0.01 kilometer, Df = 0.02 kilometer
To determine if a triangle can be formed, we need to check the inequality for all three pairs of sides:
- De + Ef > Df: 0.205 + 0.01 > 0.02 (0.215 > 0.02) - This condition is satisfied.
- De + Df > Ef: 0.205 + 0.02 > 0.01 (0.225 > 0.01) - This condition is satisfied.
- Ef + Df > De: 0.01 + 0.02 > 0.205 (0.03 > 0.205) - This condition is not satisfied.
Since the third condition is not satisfied, the set of line segments with lengths De = 0.205 kilometer, Ef = 0.01 kilometer, and Df = 0.02 kilometer cannot form a triangle.
In conclusion, not every set of line segments can form a triangle. It depends on whether the sum of the lengths of any two sides is greater than the length of the third side.