The operation process of verifying the perfect square formula using Geometric Sketchpad

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Create new parameters a and b. Open the geometric sketchpad, execute the [Data]-[New Parameter] command, enter the parameter name a in the pop-up dialog box, the value is 6, and the unit is distance. Create a new parameter b=2.00cm in this way, and execute the [Data]-[Calculate] command to calculate the value of a b.

Construct a square with the value of a b as the side length. Use the move tool to select the calculated value and execute the [Transform]-[Mark Distance] command. Use the point tool to draw any point A on the drawing board, select the point and execute the [Transform] - [Translate] command, change the angle to 0 in the pop-up dialog box, and click OK to get point B. Construct line segment AB, double-click point A to mark the center of rotation, select line segment AB and execute the [Transform] - [Rotate] command, the angle is 90, and click OK to obtain point D. Select point D and line segment AB to construct a parallel line. Also select point B and line segment AD to construct a parallel line. The intersection point is C. Construct line segments BC and CD to obtain a square ABCD.

Divide the square. Select parameter a and execute the [Transform] - [Mark Distance] command. Select point A and execute the [Transform] - [Translation] command. In the pop-up dialog box, the angle is 90, click OK to obtain point A’. Select parameter b and execute the [Transform] - [Mark Distance] command. Select point C and execute the [Transform] - [Translation] command. In the pop-up dialog box, the angle is 180. Click OK to obtain point C’. Construct a parallel line to side AB through point A’, and construct a parallel line to side AD through point C’ to obtain intersection point E. Hide the parallel lines and construct the line segments as shown below.

Calculate the area of ​​the square ABCD and the areas of the four quadrilaterals divided into it. The area of ​​square ABCD can be expressed as: (a b)*(a b), and its value can be obtained through calculation. Through calculation, it can be concluded that the areas of the four small quadrilaterals are: ab, ab, a2, b2. By calculating the areas of the four small quadrilaterals, the obtained value should be equal to the area of ​​the square ABCD, so that the completeness can be verified. Correctness of the square formula.

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