Detailed steps for constructing bisectors of interior angles of a trapezoid using Geometry Sketchpad

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For example: in the trapezoid ABCD, AD∥BC, AB=AD BC, E is the midpoint of CD. Prove: AE and BE bisect angle BAD and angle ABC respectively.

The specific operations are as follows:

1. Use the ray tool in the line segment tool and press the Shift key to draw the rays where the two bases of the trapezoid are located, and use line segments to make the waist AB of the trapezoid.

2. Use the point tool to pick a point F on line segment AB, select point A and point B, and select [Construction] - [Draw a circle with the center and points on the circumference], Construct circle B in the same way. The rays of the two circles and the two bases intersect at points D and C. Obviously, AD BC=AB.

3. Select points C and D, select [Construction]-[Line Segment] to construct line segment CD, select line segment CD, select [Construction]-[Midpoint] to construct From the midpoint E of line segment CD, use the line segment tool to construct line segments AE and BE.

4. Select points A and D, select [Construction] - [Line Segment] to construct line segment AD. Construct line segment BC in the same way, and combine circle A, circle B and point F. and two line segments are hidden to obtain a graphic that meets the conditions.

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