Math Is Fun Forum

ash2803

Member

Registered: 2019-11-10

Posts: 3

Geometry is confusing me....

Hi! I recently discovered the forum and thought it might be helpful.

I'm having trouble with a high school geometry problem.

Imagine you have been called as a expert witness in a court case.  Your expertise is in the area of planes (not airplanes, just planes in geometry).  Your task is to convince the jury that there is, in fact, a plane based on the given information.  You must prove all three of the definitions of a plane given in Lesson 1.  You may need to include some other definitions such as the definition of an angle, a ray, etc.

Question from the lawyer:  "Dr. Expert, I only see a 70° angle here.  Kelly said that having this angle means you have a plane.  I enter Exhibit A which shows three definitions of a plane.  From what I see, none of these definitions say that an angle defines a plane.  Explain how each definition proves that an angle defines a plane."

State the definition and then explain how you can prove each definition given the angle.

14. Definition 1: a line and a point not lying on the line

15. Definition 2: three points that are not collinear

16. Definition 3: two lines which intersect in a single point or are parallel

I'm not quite understanding how to describe the answers. I see that all three definitions can create an angle, but I'm not sure how to describe this?

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Geometry is confusing me....

Well, all three definitions are impossible without a plane...

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Geometry is confusing me....

hi ash2803

Welcome to the forum.

To answer your question properly I would also need to know how your course notes define an angle.  In the absence of that I assume it is "when two lines intersect they form an angle between them".  In the standard Euclidean definition that the lines are in a plane is part of the definition.

So if you use a point on one line that is not the point of intersection then you have "  a line and a point not lying on the line" so definition 1 is satisfied.

You should be able to use a similar logic for the other two.  Note: for an angle the lines are not parallel so the first half of definition 3 is needed.

In the past an on-line maths course (C-H) has asked us not to answer their actual questions.  It infringes their copyright and also gives other students clues to homework they have set.  On this forum we try to avoid just giving homework answers but will always try to help anyone who is stuck with a topic in maths. It's a tricky path to navigate.  This exact question has been asked before.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ash2803

Member

Registered: 2019-11-10

Posts: 3

Re: Geometry is confusing me....

Hi,

Ah I think I understand a little more now, I just needed an idea of how to actually describe it. I've come up with some answers now using the logic you mentioned, so we'll see how I do.

I believe you're talking about [name removed by admin to avoid helping them search for mentions]? That is the course I'm using, so I can see why you shouldn't give an actual answer. I just needed more of a hint on how to proceed, otherwise I do all my work myself (obviously, since I'm there to actually learn lol)

ash

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Geometry is confusing me....

hi ash2803

Glad to help.  There have been quite a few posts from other students of that course.  Then they complained to the site originator (MIF himself) so I've tried to tread carefully since then.  Hope you'll forgive that I slightly altered your post … I'm trying to prevent them searching for their name.  I'm hoping they've got better things to do than read every one of our posts

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ash2803

Member

Registered: 2019-11-10

Posts: 3

Re: Geometry is confusing me....

It's all good, I actually didn't think of that.

I'm sure they do have other things to do besides reading every post, but it's best to be safe lol.

ash