In addition, in particular, the following are all by hand.

In order to prevent the students who have just started to learn painting from understanding it, please explain it first. Ruler drawing refers to drawing with an uncalibrated ruler and compass. Rulers are only used to draw straight lines, compasses are only used to draw circles. Because this drawing is not affected by calculation error and scale error, it is a very accurate drawing method. The significance of drawing an arc is that because the radii of circles are equal, the distances from the intersection points to the center of the circle obtained by drawing an arc are equal, and equal line segments can be obtained.

About the ruler drawing "a point outside the straight line is the perpendicular of the known straight line", the practice is as follows:

Take point A as the center of the circle and an appropriate length (to make the arc intersect BC line) as the radius, draw the intersection line of the arc and BC.

Draw an arc with point B and point C as the center and the same appropriate length (so that two arcs can intersect) as the radius, and the two arcs intersect at point D and point E.

The straight line determined by any two points in A, D and E is the perpendicular to the straight line BC passing through point A..

The same is true for intersections on straight lines.

Because describing the vertical process is complicated, I omitted it. )

First of all, add the ruler drawing method of the second triangle found by several people downstairs.

A vertical line that intersects with point A and makes OP intersect with OP at point E..

Draw an arc with point E as the center and point AE as the radius, and intersect point OP at point D..

The vertical line where OP intersects with point d intersects with OQ at point C.

Draw an arc with point A as the center and point AC as the radius, and intersect point OP at point B..

Connecting AC, AB, BC, triangle ABC is a necessary triangle.

If it is proved, the perpendicular passing through A is CD and the perpendicular passing through F is CD.

First, it is proved that EDFA is square, and then it is proved that triangle AEB and triangle AFC are congruent through angle AEB= angle AFC=90 degrees, AE=AF, AB=AC(HL), so angle EAB= angle FAC, so angle CAB= angle FAE=90 degrees.

As for the problem that AF is greater than DO, it can be solved by changing "intercepting AF=AD" to "intercepting DF=AD" in the second step. The drawing method of ruler is as follows:

Make AE perpendicular to OP, and OP intersects e.

Draw an arc with E as the center and EA as the radius, and intersect with OP at point F..

The vertical line between OP and f intersects OQ at point B.

Draw an arc with A as the center and AB as the radius, and intersect with OP at C (take the intersection on the right side of AE).

Connect BC, and triangle ABC is the required triangle.

The proof method is to prove that triangle GBA and triangle ECA are congruent, so I won't say more about the specific method as the last one ~