Area of a 45-45-90 Triangle: Scaling with Side Length

①This interactive GeoGebra example demonstrates how the area of an isosceles right triangle (45-45-90) scales proportionally to the square of its leg length, illustrating the relationship between similar triangles and area ratios.②Core mathematical concepts include properties of 45-45-90 triangles, similarity, area formula (area = 1/2 × base × height), and the square relationship between similarity ratio and area ratio, along with ideas of linear functions and continuity.③Construction details: Using GeoGebra commands Polygon to create the triangle, PointIn for draggable points, and objects such as s (area), A, B, C (vertices), t1 (triangle), c (circumcircle), a, b (side lengths), Pointt1 (point on triangle), and text1 (text display) to enable dynamic interaction—dragging vertices updates the area and side-length ratios in real time.④Suitable for upper middle school to high school students, this example is ideal for geometry lessons or exploratory activities on similar triangle area properties, and serves as a teacher demonstration tool to visualize scaling laws.