How to operate geometric figures

Geometric figures are often used in programming, but some friends may not know how to operate them. PHP editor Zimo will introduce you to the basic operation methods of geometric figures, including creation, movement, rotation and scaling, etc., to help you solve problems in this area. Let’s learn together!

The example proposition is: Known: In the trapezoid ABCD, AD∥BC, AB=AD+BC, E is the midpoint of CD. Prove: AE and BE bisect ∠BAD and ∠ABC respectively.

The converse of this proposition is: in the trapezoid ABCD, the bisectors of AD∥BC, ∠DAB and ∠CBA intersect at point E, which is exactly on the waist CD. Then: AB=AD+BC, E is the midpoint of CD.

Obviously, we can know that ∠AEB=90°. As shown in the figure, suppose the midpoint of line segment AB is point G and connects EG, then AG=EG, that is: ∠AEG=∠EAG=∠EAD. So AD∥EG, therefore, CE=DE, AD+BC=2EG=AB.

Since the converse proposition is a true proposition, we can start from the conclusion of the proposition and draw a geometric figure that conforms to the meaning of the question. The drawing operation is as follows:

Draw the waist AB and The ray where the two bases are located. Use the [Point Tool] to draw two arbitrary points in the blank area of ​​the drawing board, and use the [Ray Tool] to draw rays through the two points respectively.

draw the angle bisectors of ∠A and ∠B, and intersect At point E. Select ∠A and ∠B in turn, execute the [Construction] - [Angle Bisector] command to construct the angle bisector,

Pick any point C on the ray where the base is located, Select the [Line Segment Tool] to draw a ray CE through point E, intersect the ray where the other base is at point D,

connect the relevant line segments, and hide the auxiliary graphics during the drawing process. You can get a graph that fits the meaning of the question.

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