1. Recall the definitions of the interior of an angle and the interior of a triangle. the interior of a triangle could have been defined equally well in other ways.
a. Explain how the interior of triangle ABC can be defined as the intersection of the three half-planes.
b. Complete the following statement to make a correct definition: "the interior of triangle ABC is the set of all points X, in the place of triangle ABC such that (1)..., (2)..., and (3)... ."
2. Is the interior of the triangle ABC completely determined by the intersection of the interiors of any two of its angles? Illustrate and formulate a definition. Is it equivalent to the previous definitions?