Isosceles Trapezium is Con-Cyclic: Construction and Proof

This GeoGebra example demonstrates the geometric theorem that an isosceles trapezium is a cyclic quadrilateral, meaning its four vertices lie on a single circle. The core mathematical concepts involved include the symmetry and equal base angles of an isosceles trapezium, as well as the circle theorem stating that opposite angles of a cyclic quadrilateral are supplementary. To construct this dynamically, the example utilizes various GeoGebra commands and objects, including Segment for drawing the sides, LineBisector and OrthogonalLine to find perpendicular bisectors and axes of symmetry, Mirror for reflecting points, and Intersect to locate the circumcenter. Angles are measured and displayed to provide a visual proof of the con-cyclic property. This interactive model is highly suitable for secondary school geometry lessons, particularly in teaching circle theorems, cyclic quadrilaterals, and geometric proofs, serving as an excellent tool for teachers and students exploring geometric constructions.