Introduction to the method of using iteration to construct triangles inscribed with midpoints in Geometry Sketchpad

For users of Geometry Sketchpad, constructing triangles inscribed with midpoints is a common challenge. PHP editor Xigua will introduce a simple and effective way to solve this problem using an iterative method. This article will guide you through the method step by step and provide clear examples to help you easily understand and apply the method.

1. Open the geometric sketchpad and create a new geometric sketchpad file. Use the [Polygon Tool] to draw any triangle ABC.

2. Select the three sides of the triangle, select the [Construction]-[Midpoint] command to construct the midpoints D, E, and F of the three sides, and connect the line segments DE, EF, DF.

3. Select point A, point B and point C in turn, select the [Transform]-[Iteration] command, and in the pop-up iteration dialog box, give the original image points A and B , C select points D, E, and F in sequence as the initial image. When you click on each midpoint, the artboard will also display the mapping results of the original image triangle iteration. Finally, click the [Iteration] button to get the midpoint triangle iteration graph.

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