Detailed tutorial on drawing the interior of a triangle with geometric sketchpad

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1. Click [Point Tool] and draw three points A, B, and C at the appropriate positions on the drawing board. Execute the [Edit]-[Select All] command, select three points A, B, and C at the same time, and execute the [Construction]-[Line Segment] command. Construct triangle ABC.

2. Click the [Move Arrow Tool] and select point B, point A, and point C in sequence. Execute the [Construction]-[Angle Bisector] command to construct the angle bisector j of ∠BAC. Click [Move Arrow Tool], click the intersection of ray j and line segment BC (status bar prompt: click to construct the intersection), and construct the intersection D of ray j and line segment BC.

3. Refer to the method in step 2 to construct the angle bisector k of ∠ABC, and construct the intersection E of the ray k and the line segment AC.

4. Select ray j and ray k at the same time, execute the [Show]-[Hide Bisector] command to hide the two bisectors. Click [Line Segment Tool] to construct line segments AD and line segments BE. Click [Move Arrow Tool], click the intersection point of line segment AD and line segment BE (status bar prompt: click to construct the intersection point), and construct the intersection point F of line segment AD and line segment BE.

5. Execute the [File]-[Save] command. Drag the vertices of triangle ABC to change the shape of the triangle. Point F is always the center of triangle ABC.

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