"If two lines intersect, then exactly one aircraft contains the lines."

Now, every line contains two points, and also according to another theorem in my book:

"If two lines intersect, climate they intersect in precisely one point."

and 3 noncollinear points specify a plane.

You are watching: Two lines intersect in more than one point

Now, a heat endlessly proceeds in two opposite directions, if two lines were to intersect, shouldn’t that develop $5$ points? and also I"m also wondering if that would produce two different planes (with both planes share one allude at the intersection.)

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edited Feb 24 "16 at 21:13

Brian M. Scott

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HTMLNoobHTMLNoob

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I think I can clear up part misunderstanding. A heat contains much more than just two points. A line is made up of infinitely numerous points. It is yet true that a heat is determined by 2 points, namely just prolong the line segment connecting those two points.

Similarly a aircraft is figured out by 3 non-co-linear points. In this instance the 3 points room a point from every line and also the suggest of intersection. We are not producing a new point when the currently intersect, the suggest was already there.

This is not the very same thing as saying the there are 5 points since there are two from every line and the point from your intersection.

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answer Feb 24 "16 in ~ 21:18

Michael MenkeMichael Menke

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Two distinctive lines intersecting in ~ one allude are included in some plane: merely take the intersection suggest and one other in each line; the three noncollinear points define a plane and the plane contains the lines.

In stimulate to see that there is no other plane containing the two lines, an alert that any such aircraft necessarily has the three previous points and since 3 noncollinear points specify a plane, it must be the aircraft in the previous paragraph.

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answered Feb 24 "16 at 21:18

man BJohn B

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First, a line includes infinitely many points. The idea right here is the if you have actually two unique lines i m sorry intersect, over there is just one (unique) aircraft that has both currently and all of their points.

Try visualizing a airplane that includes two intersecting lines:

Notice the if you then shot to "twist" that plane in some method that it will certainly no longer contain both lines. In other words, there is no other airplane that can contain both lines, over there is just one.

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answer Feb 24 "16 in ~ 21:19

CarserCarser

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Think the a chair"s 4 legs. To examine that the 4 legs have the very same length. Pull 2 strings connecting pairs of opposite legs, every string is attached at the bottom that the legs. If the strings touch each various other in the center then the chair is secure (the one plane), otherwise that is wobbly (no plane).

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reply Feb 24 "16 at 21:27

Oskar LimkaOskar Limka

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