To Be or Not to Be

Determine if the following groups can represent the side lengths of a triangle. If yes, then describe the triangle. If not, then explain why.


In order to create a triangle, what must be the relationship between the side lengths? Explain your reasoning.

The integers 2 through 7 are placed into a hat. If three integers are randomly selected without replacement, then what is the probability that they can form the sides of a triangle? How would the results change if the integers were randomly chosen with replacement?