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A straight line can intersect the side of a convex quadrilateral in at most two points and so divided it into at most two segments. A concave quadrilateral (an arrowhed or chevron) can be divided into three if the line touches the reflex vertex and cuts off the two "barbs" of the arrowhead. But 4 triangles is not possible.

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Q: How do you draw a quadrilateral so when you draw a straight line you get 4 triangles?
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How do you make four triangles out of a quadrilateral by a line through it?

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.


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If you accept that the sum of the angles in a triangle is 180 degrees, then picture this. A quadrilateral shape is two triangles. If you draw a line between one pair of opposite corners in quadrilateral shape, you have two triangles that share a common side. The sum of the angles in the quadrilateral must equal the sum of the angles in the two triangles. 2 x 180 = 360


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