Interactive Triangle Area Exploration (cf. Parallelogram)

① This applet allows students to drag the vertices of a triangle anywhere on the canvas, dynamically revealing the relationship between the triangle's area and that of a related parallelogram, enabling meaningful discovery of the area formula. ② Core mathematical concepts include the triangle area formula (base × height ÷ 2), comparison with parallelogram area (base × height), and geometric transformations such as rotation and midpoint construction, emphasizing area conservation. ③ Construction highlights: using GeoGebra commands Polygon to create triangle poly1, Midpoint and Rotate to generate a rotated copy poly1', and Segment to connect vertices forming a parallelogram; key objects include A, B, C, D, α, A', B', C', and a button (button1) for animation or reset. ④ Suitable for middle school geometry classes or advanced elementary math, ideal for teacher demonstrations or student-led inquiry, fostering geometric intuition and deductive reasoning about area formulas.