Exploring Equal Areas of Triangles with Same Base and Height

① This applet demonstrates a fundamental geometric fact: triangles sharing the same base and height have equal areas, even when the apex moves along a line parallel to the base. ② Core mathematical concepts include the triangle area formula (Area = 1/2 × base × height), the property of equal base and height, constant distance between parallel lines, and the invariance of area under vertex translation. ③ Construction details: using GeoGebra commands such as Point, Segment, Intersect, Midpoint, Polygon, and Text to build the triangle, its base, and altitude; sliders or buttons (button1, button2) allow the apex to slide along a parallel line, while dynamic area labels (arealabel, text1, etc.) update in real time; auxiliary objects like mid, midheight, eq1, eq3 mark midpoints and heights for clarity. ④ Suitable for middle school geometry classes or advanced elementary students, this interactive tool helps learners intuitively grasp the derivation of the triangle area formula and the property that triangles with equal base and height have equal areas, making it ideal for teacher demonstrations or student-led exploration.