Is it axiom that the distance between parallel lines is equal everywhere?

Is it axiom that the distance between parallel lines is equal everywhere?

Yes!

The parallel line on one side of a triangle determines the theorem
If the points D and E are on the sides AB and AC of the triangle ABC respectively, if de / BC = ad / AB, can we get de parallel to BC? Why?

Not necessarily. First of all, De is parallel to BC, and then de / BC = ad / AB can be obtained
However, if ∠ C > A, then the f point can be obtained on AE, so that ∠ DFE = ∠ def
So DF = De, there are DF / BC = ad / AB, but DF is not parallel to BC
So we still need to consider the relationship between internal angles

"The property theorem of parallel lines on one side of triangle" is not understood at all! It's really hard to think clearly!
The theorem is as follows: a line parallel to one side of a triangle cuts the lines on the other sides, and the corresponding line segments cut are proportional
A straight line cuts another straight line. How can a straight line cut a line segment
What kind of corresponding line segment is the corresponding line segment
Proportionality? What is proportionality? What is proportionality!
This theorem really entangles me! I am too stupid!
The theorem is wrong. It's parallel to the triangle

Just draw a picture
As shown in the figure: make a straight line de ∥ AC and intersect AB, BC at D and e respectively, then the triangle ABC ∥ triangle DBE (this need not be proved), so AB: DB & nbsp; = & nbsp; BC: be & nbsp; = & nbsp; AC: de & nbsp; - this is "corresponding edge proportion", that is, the similarity ratio of two similar triangles

What triangle's trilateral relation, trilateral theorem, trilateral relation inference?
There is a summary under a topic, which says: to prove the unequal relationship of line segments, we generally use the trilateral relationship of triangle, if the size relationship of sum, we use the trilateral relationship theorem, if the difference relationship, we use the trilateral relationship inference

Let three sides be a, B, C, then there is
a+b>c
a+c>b
b+c>a
This is the trilateral relation theorem
a> B-C > B-A, b > a-c is the inference of trilateral relation