Prove that straight lines A and B have only one intersection.
reductio ad absurdum
Proof: suppose that straight lines a and b intersect more than one intersection o,
Then a and b have at least two intersections o and p. At this point,
A straight line a is a straight line determined by two points o and p,
Line b is also a line determined by o and p.
In this way, two straight lines are determined by o and p.
This contradicts the postulate 1 in Elements of Geometry: two points can only determine a straight line.
∴ Two straight lines intersect and there is only one intersection.
(2)
1。 Judgment of previous certificate (SSS)
Is it possible that the triangles AC = AD, BC = BD and AB = AB in the diagram do not overlap?
No way! Suppose it is possible!
Angle ADC= angle ACD
Angle BCD= angle BDC
Angle ACD= angle ADC
So the angle ACD
conflict
So (SSS) judgment is established.
2。 Geometric elements postulate 3: just a little, make a circle with a fixed length.
Make a circle with a fixed length at a point outside the line and cross the straight line.
There are two intersections, and then make a midpoint on that straight line to connect the center of the circle and the midpoint.
Judging from (SSS), the two angles are equal and the sum is a right angle, so the point outside the straight line can reach the known point.
This line is vertical.
3。 Prove the judgment of parallel lines: the internal angles on the same side are complementary and the two straight lines are parallel.
If they are not parallel, then the extension can intersect the inner angle and the inner angle of the triangle on the same side.
And greater than 180.
So the inner angles on the same side are complementary, and the two straight lines are parallel.
4。 Two perpendicular lines made by points outside the line parallel to a straight line.
Two straight lines drawn through a certain point cannot be parallel (parallel definition)
So in the same plane, a little beyond the straight line, there is only one straight line, just like the original one.
Know that the straight line is vertical (in the plane).