Construction and Properties of Triangle Altitudes

①This example demonstrates how to construct the altitudes (perpendicular segments) of a triangle in GeoGebra, showing that the three altitudes intersect at a single point (the orthocenter). ②Core mathematical concepts include triangle altitudes, orthocenter, and special properties of altitudes in equilateral and isosceles triangles, along with the use of rational numbers and fractions in coordinate representation. ③Construction details: The Segment command is used to draw line segments, the Polygon command creates triangle poly1, with vertices defined by objects A, B, and C; perpendicular lines are constructed to obtain altitudes a_1 and b, resulting in a complete altitude diagram. ④Suitable for middle and high school students learning triangle properties, geometric construction, and dynamic geometry software operation, useful for classroom demonstrations or independent exploration of the concurrency of altitudes.