I"m i m really sorry if this is one extremely basic question, however I"m honestly having actually a hard time knowledge a organize in my geometry book. Below is the theorem:

"If 2 lines intersect, then specifically one airplane contains the lines."

Now, every line consists of two points, and according to one more theorem in mine book:

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

and three noncollinear points define a plane.

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

Now, a line endlessly continues in 2 opposite directions, if two lines were to intersect, shouldn’t that produce $5$ points? and I"m additionally wondering if the would develop two various planes (with both planes share one suggest at the intersection.)


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edited Feb 24 "16 in ~ 21:13
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Brian M. Scott
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asked Feb 24 "16 in ~ 21:06
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I think I can clear up part misunderstanding. A heat contains more than simply two points. A line is made up of infinitely countless points. It is however true that a line is figured out by 2 points, namely just prolong the line segment connecting those two points.

Similarly a plane is determined by 3 non-co-linear points. In this case the 3 points space a point from each line and also the allude of intersection. We are not producing a new point once the currently intersect, the allude was already there.

This is not the exact same thing as saying the there are 5 points because there space two from each line and also the point from their intersection.


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answer Feb 24 "16 in ~ 21:18
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Michael MenkeMichael Menke
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Two unique lines intersecting at one point are had in some plane: just take the intersection suggest and one various other in every line; the three noncollinear points define a aircraft and the airplane contains the lines.

In bespeak to check out that over there is no other airplane containing the two lines, an alert that any type of such plane necessarily contains the three former points and since three noncollinear points specify a plane, it have to be the plane in the previous paragraph.


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answered Feb 24 "16 in ~ 21:18
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man BJohn B
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First, a line includes infinitely numerous points. The idea here is that if you have actually two distinctive lines i m sorry intersect, over there is just one (unique) airplane that has both present and every one of their points.

Try visualizing a airplane that consists of two intersecting lines:

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Notice that if you then try to "twist" that airplane in some method that it will no longer contain both lines. In various other words, over there is no other aircraft that might contain both lines, there is only one.


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answer Feb 24 "16 at 21:19
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CarserCarser
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Think of a chair"s 4 legs. To check that the 4 legs have actually the exact same length. Pull 2 strings connecting pairs of opposite legs, each string is attached at the bottom that the legs. If the strings touch each various other in the middle then the chair is secure (the one plane), otherwise it is wobbly (no plane).


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answered Feb 24 "16 at 21:27
Oskar LimkaOskar Limka
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