A parallel B, B parallel C, why A parallel C

If a and c are not parallel, then a and c intersect.

Because A and B are parallel, B and C intersect.

contradicts what is known.

You go and find two square things, side by side, and you understand.

In the final analysis, this involves the assumption of Euclidean geometry (i.e., geometry as we usually learn) that there is and only one straight line parallel to the known straight line at a point outside the line. That is, the famous Fifth Public Vacant Problem.

This cannot be proven or denied within Euclidean geometry.

If we change this assumption, there can be multiple lines parallel to the known straight lines at a point outside the line. then we can come up with a complete and harmonious geometric system, and there is no contradiction within it. That's when your topic is wrong.

Historically, many famous mathematicians such as Lobachevsky, Gauss, Riemann, etc., have studied this problem and produced non-Euclidean geometry (Lobachevsky geometry, Riemannian geometry, etc.). Moreover, Einstein's general theory of relativity coincides with non-Euclidean geometry, and when Einstein studied general relativity, he struggled to have an ideal mathematical tool to solve the problem, and later found that Riemannian geometry could solve it, so he buried himself in hard study for several years.

So you can't prove it in that question, but it's clearly true in Euclidean geometry. It can be used directly when doing the questions.

A is parallel to B, no. In its entirety, a is parallel to b is inaccurate, because they actually have three possibilities: parallel, coincident, or straight lines with different planes.

It is divided into three cases: when two straight lines are in the same plane and do not coincide, line A is parallel to line B, when two lines are in the same plane and coincide, line A and line B coincide, and when two lines are not in the same plane, line A and line B are straight lines on different planes.

This question examines the parallel lines of the slag sedan car.

Note: In the same plane, two straight lines perpendicular to the same line are parallel. Pay particular attention to the prerequisites.

Parallel nature:The two parallel lines are truncated by a third straight line, with the same inner angles.

Complementarity (referred to as "two straight lines parallel, as in the same side as the angle complementary").

The two parallel lines are truncated by a third straight line, with the wrong angles inside.

Equal (abbreviated as "two straight lines parallel, with equal internal wrong angles").

The two parallel lines are truncated by a third straight line, at the same angle.

Equal (abbreviated as "two straight lines parallel and equal at the same angle").

There is only one and only one straight line parallel to the straight line (parallel axioms).

If two straight lines are parallel to each other, then the two lines are also parallel to each other.

The distances between parallel lines are equal everywhere.

Set the Cartesian coordinate system in a two-dimensional plane.

There are three non-coincident straight lines a, b, and c, and the corresponding functions are f(x), g(x), and h(x), and a is parallel to b, and a is parallel to c, and a is parallel to c, and the definition of parallel is that two disjoint straight lines in the two-dimensional plane we call them parallel, because a is parallel to b, so the slope of a and b is the same, that is, f'(x)=g'(x)=k, and f'(x)=h'(x)=k, so g'(x)=h'(x)=k, and the slope of b and c is the same, Let the line b be g(x)=kx+b, the line c is h(x)=kx+c, b and c are the ordinates of the focus of the line b, c and y axis respectively, b and c do not coincide with Zen Ming, so b is not equal to c, and the functional expression of the line b and c is expressed.

The system of column equations is solved, and x has no solution, so the lines b and c have no intersection in the two-dimensional plane, which meets the definition of parallelism, so b and c are parallel. Note: If the slope of two straight lines in a two-dimensional plane.

In contrast, a system of equations must give a set of x and y so that the group of equations is true, indicating that two lines intersect at that point (x,y).

If the straight line A is parallel to B, and B is flat and dust is C, then the theoretical basis of A parallel C is the axiom of parallelism and its corollary.

Parallel axiom: There is only one straight line parallel to the known straight line.

Axiom corollary: If both lines are parallel to the third line, then the two lines are also parallel to each other.

Make a straight line and intersect a b c, and determine the corresponding isotope angle equality through a parallel b and b parallel c.

Then prove that a is parallel to c according to the equality of the corresponding isotope angles

There is a picture to explain the start of the lease in more aspects.

For example, a quietly calls b at an isotope angle of 1= 2, and in the same way b c isotope angle 2= 3

So 1= 3 isotope type spring equal 2 straight lines parallel so a c

A parallel B, B parallel C

a c (two parallel lines parallel to the same line).

If A is parallel to B, A is parallel to C, then B is parallel to C, proving its correctness.

Proof: If a b, a c, then b c proves: if b and c are not parallel, then b and c intersect at one point o and because a b, a c there are two thick straight lines b and c parallel to a, which contradicts the axiom of parallelism, so the assumption is not true.

Straight lines A, B, C are in the same plane of the same mold, A and B are parallel to each other, A and C are parallel to each other, then B and C are parallel to each other.

So the answer is: parallel

A is perpendicular to B and A is perpendicular to C, so B is parallel to C is right to assume that the slope of the straight line A is A1, the slope of B is B1, and the slope of C is C1, and when the two lines are perpendicular, the slopes are multiplied equals -1; When two lines are parallel, the slope is equal to a perpendicular to b then a1*b1=-1, a perpendicular to c then a1*c1=-1, and the division of the two equations gives b1 c1=1 =>b1=c1

So B is parallel to C

In a plane, a b, b c, two straight lines are parallel, and the isotopic angles are equal, so the angle between a and b and the angle between a and c are equal, that is, a c

If it is not in a plane, the angle between a b, a and b is 90°

The angle between b c, b and c is 0, that is, c can be translated to the straight line b, at this time b a, so c a

There is a premise here, and that is to be in a plane. If they are not in the same plane, b and c may be straight lines on opposite planes.

Wrong. Only a, b, and c are held in the same plane.