Pythagorean (Pythagoras) Theorem Demo Using Isosceles Triangles and Tangent Line

This example demonstrates the Pythagorean relationship through a constructed geometric configuration that uses isosceles triangles and tangent-line interpretations to visually link angles, tangents, and side-length relations. The key mathematics includes the Pythagorean Theorem (a square-length relation among the sides of a right triangle), the geometric meaning of the tangent function, and how isosceles-triangle symmetry supports consistent angle/side correspondence. Construction-wise, it relies on GeoGebra primitives such as Point (defining construction vertices like O, A, B, C, D and additional auxiliary points), Segment (connecting relevant points to form sides and supporting lines), Polygon (building multiple triangle/region outlines like poly1–poly4), and arrow2 (adding directional markers/annotations for the tangent or corresponding segments). With labeled objects (e.g., pic1/pic2 and text1) the diagram emphasizes the mapping from trigonometric/tangent features to the theorem’s measurable length relations. Suitable for middle to high school geometry lessons, theorem visualization in classrooms, and instruction that connects trigonometry (tangent) with classical geometry.