Property of the Altitude to the Hypotenuse in a Right Triangle

① This example demonstrates the altitude drawn from the right-angle vertex to the hypotenuse in a right triangle, and its key geometric properties, including the similar triangles formed with the hypotenuse and the two legs. ② The core mathematical concept is the right-triangle projection theorem (Euclid's theorem), stating that the altitude to the hypotenuse divides the triangle into two smaller right triangles similar to the original, and that the altitude is the geometric mean of the two segments of the hypotenuse. ③ Construction details: using GeoGebra commands Rotate, Angle, and Polygon to build the right triangle, OrthogonalLine to draw the perpendicular to the hypotenuse, Intersect to find the foot H, Segment to connect the altitude and the hypotenuse segments, and text objects to label angles and lengths. ④ Suitable for upper middle school or early high school students, this interactive figure helps visualize the altitude property, similarity of triangles, and the projection theorem, and can be used for classroom demonstration or self-directed exploration.