Wordless Proof of Pythagoras for the 1:3 Leg-to-Hypotenuse Ratio

This GeoGebra example is a wordless-style construction that visually confirms the Pythagorean Theorem in the special case where a leg to hypotenuse has a fixed ratio of 1:3. It demonstrates how the identity a^2 + b^2 = c^2 can be “read” from the geometric arrangement under a prescribed length proportion. Key concepts include the Pythagorean Theorem, circle-based constructions tied to angle/orthogonality relationships, and triangle geometry with midpoints and preserved length structures. Construction highlights: it uses Intersect and Point to create critical intersection points; Line and Circle to define supporting lines and circles; CircleArc to render essential arc components; Midpoint to set midpoint anchors; and Translate together with Rotate to manually move and rotate figures into a configuration consistent with the 1:3 ratio. Polygon and Angle are used to form composite shapes and to emphasize the geometric constraints that make the theorem apparent. Suitable for middle/high school learners, classroom demonstrations, and exploratory geometry/proof activities.