to bisect an angle means to cut it in half
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bisect means to cut into 2 equal parts.
Bisect means to cut something in to two pieces.
it depends on what you mean by a diagonal. If you take a diagonal to mean a line from one corner to the "opposite" corner, then a nonagon doesn't have any, and a decagon has five. The reason a nonagon doesn't have any, is that the corners aren't opposite each other.
Basically the definition of bisect is to separate two parts of a line segment to create two congruent line segments, which leads to them being equal.
This assumes you mean a regular octagon. There are 4 pairs where the diagonals each skip two vertices. Then there are 4 sets of three parallel diagonals where one is the main diagonal (skips three vertices) and two skip just one vertex. For each of these sets of three, you can choose three pairs of two. That makes 12 pairs all up. So there are 4 + 12 = 16 pairs.