Detailed method for verifying the sum of acute angles of a right triangle using Geometric Sketchpad

1. Create a new geometric sketchpad file. Use the [Line Segment Tool] to draw straight line AB, select point A and line segment AB, and select the [Construction]-[Perpendicular Line] command. Pick any point C on the vertical line. Hide vertical lines. Draw line segments AC and BC.

2. Set the line type of line segments AB, BC, and AC to [dashed line]. Select the [Construction]-[Midpoint] command to draw the midpoints D, E, and F of the three line segments.

3 Construct line segments AD, DE, EF, and FA and set the line types of line segments AD, DE, EF, and FA to [solid line]. Draw points G and H arbitrarily outside the right triangle ABC, and draw line segments GF, GE, HE, and HD.

4. Select points G, C, H, and B in sequence, and select the [Edit]-[Operation Button]-[Move] command. Change the button label to [Restore]. Select any point on the artboard and name it I. Select points G, A, H, and I in turn, and select the [Edit]-[Operation Button]-[Move] command. Change the button label to [Collapse].

5. Draw a point L near the right-angled vertex A, and draw two straight lines passing through the point L and parallel to the line segments AB and AC, respectively. AB intersects at point M and straight line AC at point N. Hide the two straight lines. Draw line segments LM, LN, and hidden points L, M, N. This will draw the right angle mark.

#6. Select points A, B, and C, select the [Construction]-[Triangle Interior] command, and fill the interior color of triangle ABC with yellow. Construct the interior of the quadrilateral ADEF, triangle GEF, and triangle HDE respectively, and fill them with another color.

7. Select points I and A, select [Edit]-[Operation Button]-[Move] command, and use the default value. Click this move button once to hide it. Select the [File]-[Save] command.

When you click the [Restore] button, the effect as shown in the picture will appear.

When you click the [Collapse] button, the effect shown in the picture will appear.

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