Final answer:
The answer explains the criteria for constructing triangles and probabilities related to dice. It also touches on geometrical probability and its implications.
Explanation:
The criteria for constructing triangles are:
- Three sides: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Two angles and a side: The side must be between the two angles, satisfying the law of sines.
- Side-Angle-Side or Angle-Side-Angle: The side and the non-included angle must satisfy certain conditions.
When discussing probabilities related to dice, the outcomes are equally likely. For instance, the probability of rolling an odd number on a fair six-sided die is 3/6 or 1/2.
Geometrical probability involves determining the likelihood of events in geometric settings, such as random lines in shapes like circles, where different hypotheses lead to varied results.
Learn more about Triangle construction and dice probabilities here:
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