Lesson 7.3 - Geometric Mean (Right Triangle Altitude Theorem)

①This example demonstrates the geometric mean relationship in a right triangle: the altitude to the hypotenuse divides the hypotenuse into two segments, and the altitude is the geometric mean of those segments; each leg is also the geometric mean of the hypotenuse and the adjacent segment.②Core mathematical concepts include geometric mean, similar triangles, mean proportional, and the right triangle altitude theorem (Euclidean theorem).③Construction highlights: using GeoGebra commands such as Segment, OrthogonalLine, Point, Intersect, Angle, and Distance, a right triangle ABC is constructed with altitude AD to the hypotenuse, and segment lengths (distanceAD, distanceDC, distanceDB, distanceBA, distanceBC) are measured and displayed via text objects (TextAD, etc.) to verify the geometric mean relations.④Suitable for upper middle school or high school geometry classes, this interactive tool helps students intuitively grasp the geometric mean and the right triangle altitude theorem, and can be used for exploratory learning.