we know that if we have two lines that are parallel, so let me draw those two parallel lines, l and m
so that's line l and line m
we know that if they are parallel, then, if we were to draw transversal that intersects both of them
that the corresponding angles are equal, so this is x and this is y, so we know that if...if
l is parallel to m, then...then x is equal to y.
What I want to do in this video is prove it the other way around.
I want to prove, so this is what we know, we know this, what I want to do is prove
if x is equal to y, then l is parallel to m, so that we can go either way
if they are parallel then the corresponding angles are equal and i want to show that if the corresponding
angles are equal, then the lines are definitely parallel.
What I'm going to do is prove it by contradiction. So let's put this aside right here, this is our goal
I'm going to assume this isn't true, I'm going to assume it's not true
I'm going to assume that x is equal to y
and l is not parallel to m, so let's think about what type of reality
that would create, so if l and m are not parallel and they are different lines
and they are going to intersect at some point
this is line l, let me draw m like this, they are going to intersect.
By definition if two lines are not parallel, they are going to intersect each other
and that is going to be m and this thing that was a transversal I'll just draw it over here
and then this is x, this is y, we're assuming that y is equal to x so we could also call the measure
of that angle x. So given all this reality and we're assuming that in either case, that this is some
distance that this line is not of zero length so this line right over here is not going to be of zero length
or this line segment between points a and b I guess we could say AB the length of that line
segment is greater than zero I think that's a fair assumption in either case
AB is going to be greater than zero
So when we assume that these two things are not parallel, we form ourselves a nice little triangle
where AB is one of the sides and the other two sides I guess we can call this point of intersection

證明 - 同位角相等意謂著兩線平行 (英)

證明 - 同位角相等意謂著兩線平行 (英) : 利用反證法證明同位角相等，兩線就平行