The example course of drawing geometry from the conclusion of the Geometry Sketchpad

Before the tutorial we gave examples of the proposition: known: trapezoid ABCD, Ad∥bc,ab=ad+bc,e is the midpoint of the CD. Verification: AE, be divided equally ∠bad, ∠abc.

The converse proposition of the proposition is: in the trapezoid abcd, the Ad∥bc,∠dab and the ∠CBA of the intersection point E, and point e happens to be on the waist CD. Then: Ab=ad+bc,e is the midpoint of the CD.

Obviously, we can learn about ∠aeb=90°. As shown in the following figure, the midpoint of the segment AB is the point G, which is connected with EG, then Ag=eg, namely: ∠aeg=∠eag=∠ead. So ad∥eg, therefore, Ce=de,ad+bc=2eg=ab.

Drawing validation conclusion Examples in a geometric artboard

Since the inverse proposition is a true proposition, we can set out the conclusion of the proposition to draw the geometry that conforms to the question, and the drawing steps are as follows:

Step one to draw the ray of the waist AB and the two bottoms. Use the Point tool to draw any two points in the blank area of the artboard, using the Ray tool to paint the rays at two points, as shown in the following figure.

A sample of the waist and bottom rays of a trapezoidal drawing in a geometric artboard

Step two as ∠a and ∠b angle of the line, at point E. Select ∠a and ∠b in turn, perform the "construct"-"angular divide line" command, and construct the angular split line, as shown in the following figure.

Example of drawing ∠a and ∠b angles in a geometric artboard

Step three at the bottom of the ray takes up a little C, select "Segment Tool" over the point e as a ray CE, to the other end of the ray at point D, as shown in the following figure.

To paint the X-ray CE sample in a geometric artboard

Step four links the related segment, and the drawing process of the auxiliary graphics hidden, you can get the graphics.

To paint the X-ray CE sample in a geometric artboard

From the above examples, it can be seen that the problem of plane geometry mapping usually can be attributed to the location of certain points, and the position of a point is often determined by two conditions.