A polygonal device for teaching students who prefer kinesthetic learning methods is presented in which the polygonal device can represent two-dimensional polygons of varying shapes and sizes. One or more of the sides, or legs, of the polygonal device are extendable, and the angles of the polygonal device may be manipulated to a desired angle. The devices presented include, but are not limited to, triangles, quadrilaterals, parallelograms, rectangles, squares, trapezoids, and kites. In each of these devices, the legs of the device are non-detachable, i.e. the device does not come apart during normal manipulation and operation.