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I am having a problem constructing this square for some reason as i am not sure where to put the point X:

Let ABCD be a square and X a point such that A and X are on opposite sides of CD. The lines AX and BX intersect CD in Y and Z respectively.

Is CD perhaps a diagonal? If so how can BX intersect CD in Z. If it is not a diagonal: Where must X be i.e. what are the opposite sides of X? and if they are not diagonals again how can BX intersect CD?

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up vote 1 down vote accepted

Usually if a polygon is named like ABCD then it means that its vertices are A, B, C and D, and you meet each vertex in that order by walking along the edges of the polygon (usually anticlockwise). So CD is not a diagonal; AC and BD are diagonals.

The picture I have in my head from your description is something like this: enter image description here

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