Trig Identities from Similar Right Triangles (I)

This GeoGebra example constructs two similar right-triangle configurations to demonstrate how trigonometric identities follow directly from geometric similarity and angle definitions. It highlights sine/cosine/tangent relationships in right triangles and uses the correspondence of sides between similar triangles to build and visualize the resulting trig equations. Key math concepts include similarity of triangles, right-triangle trigonometric definitions, angle measurement (such as θ and related angles α, β), and proportion-based reasoning that turns geometric constraints into trigonometric equalities. The construction relies on GeoGebra commands indicated in the construct summary: Point and Circle to place key points and define circular elements; Line, Ray, and Segment to draw triangle sides and auxiliary lines; OrthogonalLine to enforce right angles; Angle to label and control the key angles; and Intersect to locate dependent vertices that complete the similarity structure. The listed objects (multiple labeled vertices, auxiliary segments, radius, and text labels) support a visual proof workflow. Suitable for high-school to early undergraduate trigonometry, especially for intuitive instruction and exploratory verification of trig identities.