One possible term is the seam.
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its called the intersept point when they don't meet its called a parallel line
They are not parallel if they meet. The only other possibility may be if they are the same line, in which case they are parallel, and meet in the distance (though there is no distinguishing one from the other).
It depends what shape the lines meet in. If they meet in a triangle the point in which the lines meet are called the vertex.In Geometry, this isn't precisely true, since there are no "lines" in a triangle, only line segments.In Euclidean (standard) geometry, two lines can only:(a) meet at a single "point"; OR(b) never meet (they are parallel lines).You could ask "what if they meet at several points?". In that case, there is just one line. A line goes on infinitely far in either direction. And if two lines meet at more than one point, they are congruent at every point, and are therefore both just the same line. It is impossible for two different lines to meet at two or more points in Euclidean geometry.
The median of a triangle is a straight line from a vertex to the midpoint of the opposite side. The three medians of a triangle meet at the centroid. If the triangle is made of uniform material the centroid is the centre of mass of the triangular shape.