Jellopudin 2 years ago Do 2 intersecting lines lie in 2 planes?

1. Directrix

2. Directrix

@Jellopudin

3. Jellopudin

i belive yes, in my mind and how im seeing it play out in my brain it looks like there are two sperate planes

4. Jellopudin

Im 16 trying to graduate this summer :)

5. Directrix

Okay. I'll draw two intersecting lines and make a case for exactly one plane. Hold on.

6. Directrix

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7. Jellopudin

LOL I made a fool of my self, thanks for helping! I was thinking of the totally wrong thing ;0

8. Jellopudin

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9. Directrix

You did not make a fool of yourself. And, my argument may be incorrect.

10. Jellopudin

No, cause two intersecting lines can never create 2 different planes

11. Jellopudin

There has to be a 4th demension ;)

12. Directrix

Here's my thinking: Line XY intersects line ZX at point X. Points X, Y, and Z are not on the same line. They are non-collinear points. By the axioms, three non-collinear points determine a unique plane. Therefore, exactly one plane contains the two intersecting lines.

13. Jellopudin

Thanks :)

14. Directrix

What do you think? Now, if we ask if 3 intersecting planes lie in exactly one plane - well, that's a different story.

15. Jellopudin

yeah i know haha, im using my arms and a piece of paper to figure it out :P

16. Directrix

I use pencils and pens or whatever is handy. Visualization is so important in Geometry.

17. Jellopudin

Totally agree

18. Jellopudin

You have to agree haha

19. Directrix

Hey what about this: Do a line and a point not on the line lie in exactly one plane?