Yes
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Yes, any quadrilateral has diagonals.
They make four triangles, not a triangle.
If the diagonals of a quadrilateral are perpendicular to each other, then the quadrilateral is a square.Or a kite.
A quadrilateral has 2 diagonals. It does not matter whether it is convex or not.
You cannot make four triangles our of a quadrilateral by ONE line through it. One line can give you at most two triangles. Two lines, each running from one vertex of the quadrilateral to the opposite vertex, will give 4 triangles.