The Master thesis examines properties of convex and concave quadrilaterals. Firstly, it studies a shape that is formed by the midpoints of a quadrilateral. Then it deals with significant points in a quadrilateral such as centroid, orthocenter, circumcenter and nine-point center, and proves that aforementioned points lie on the same line. Furtheron, the thesis focuses on the triangles, whose vertices are determined by three out of the four vertices of a quadrilateral. It defines the point that lies on nine-point circles of these triangles. In the second part, this point is independently discussed for the case of cyclic quadrilaterals. In addition, the master thesis describes incenters in a convex quadrilateral, and states a formulation for the area of a convex quadrilateral. At the end, it addresses the similarities of quadrilaterals with additional thought on cyclic quadrilaterals.
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