Conjecture:If two parallel lines are cut by another line, then pairs of corresponding angles are _____.?

Question

I really don't get that conjecture. :/ Help?

Answer 1

Then the two opposites are equal. this is a conjecture in that it relies in part on circular reasoning, or is a "self-consistent" postulate(ie you must assume it is true in order to prove it). The implications of this is that parallel lines, if extended to infinity, will not cross or diverge.

However it is possible to imagine a situation where parallel lines do converge, (like on the surface of a globe for example) or where parallel lines diverge; but the former requires quite a few mathematical tricks to accomplish, and the latter violates a number of fundamental principles of geometry (the Pythagorean theorem for example). Both these cases require that space has a "curvature" (as in general relativity) and that the total curvature is not equal to zero.

This may in fact be the case for our universe, but so far at least in the visible universe this is not thought to be true.

So in short, best to stick to plane, or Euclidean geometry for the present.

Answer 2

Equal. Consider 2 parallel roads, and a third road (which is straight) at some random angle. Two intersections will be created. The Northeast corners will have the same angle, as will the NW, SE, SW corners. These are the corresponding angles.

Answer 3

Conjecture:If two parallel lines are cut by another line, then pairs of corresponding angles are equal_____?

Answer 4

congruent (have equal measure).

A line has a constant slope... so when it cuts through the first parallel line it forms a certain angle. When it goes through the parallel line, it forms that same angle.

So the corresponding angles are congruent (or equal).

Answer 5

congruent, the correct conjecture is: If two parallel lines are cut by a transversal, then the corresponding angles are congruent

Answer 6

equal