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#1 2012-08-30 08:45:57

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Naming Geometry Elements

Hi,

I am starting my geometry course this year and my first lesson is about Naming Geometry Elements.

I understood what  Point, Line Segment,  Line, Ray, and  Angle are but am really stuck on what
plane is I know it is defined by three points not lying on a line.

does anybody have a video to explain what that is ?

and also I answered these two questions I was wondering if they are correct

For #1- I answered (C)

#1- We need two points to define a line.  A different way to say this is that if you have two points, you will need at least a line to hold them.  In this sense, what do you need at least three points to define?

A-three lines
B-a ray
C-an angle or a plane
D-a line or an angle
E-a line segment
F-a point

#2- I answered (A)

2. Two points define a line, but if there are two lines in a plane, and if they intersect somewhere, they “define” a single point.  If there are two planes in space, and they intersect, what do they define?  (Look at the walls of your room, where they meet. Imagine if there were no floor or ceiling, and the walls went up and down and side to side forever, what would the corner where they meet look like?)

A a ray
B a line
C a point
D a plane
E  a partridge
F  a pear tree


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#2 2012-08-30 08:57:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Naming Geometry Elements

Hi zee-f

Sorry for off-topic posting, but welcome back! Haven't seen you in a long time!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2012-08-30 09:03:42

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

Thanks anonimnystefy smile.... I miss this forum soooooooo much  it makes math a wonderful adventure. I am so exsited in starting my geometry cource this year.


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#4 2012-08-30 09:53:45

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Naming Geometry Elements

Hi zee-f

You're welcome.

Regarding the first question, I think it is very ill-posed and if I understand it correctly, it has multiple answers. Is that the question word to word?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2012-08-30 10:12:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,718

Re: Naming Geometry Elements

Hi zee-f;

Long time no see!

but am really stuck on what
plane is

Think of a plane as a thin sheet ot paper that is infinitely long and wide.

View Image: 2012-08-30_150918.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#6 2012-08-30 10:13:50

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

yes, it has multiple answers, yeah it is   the question word to word

We need two points to define a line.  A different way to say this is that if you have two points, you will need at least a line to hold them.  In this sense, what do you need at least three points to define?


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#7 2012-08-30 10:20:45

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Naming Geometry Elements

Well, they can define either a plane, an angle or 3 lines.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#8 2012-08-30 10:23:31

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

So a plane is a a flat surface going on forever and we need three points to make it.


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#9 2012-08-30 10:25:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,718

Re: Naming Geometry Elements

Hi;

A series of 3 points will always determine a plane unless 2 or all 3 points are identical points (they have the same coordinates).Or as long as the three points do not lie on a single line.

New avatar I see.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#10 2012-08-30 10:33:09

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

thank you I understand it better now.

yup I love kittens your avatar looks amazing too.


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#11 2012-08-30 10:34:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,718

Re: Naming Geometry Elements

Back to school!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#12 2012-08-30 11:05:36

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

No I study online so I dont really have a break


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#13 2012-08-30 11:26:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,718

Re: Naming Geometry Elements

Hi zee-f;

That is even better. I should have remembered that. How do you like geometry?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#14 2012-08-30 12:11:15

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

It's my first year taking geometry, but the first lesson sound fun.


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#15 2012-08-30 12:23:56

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

I started working on my first lesson I answered these questions I was wondering if they are correct. I skipped the numbers am still working on.

#2- I choose (A)

2. Two points define a line, but if there are two lines in a plane, and if they intersect somewhere, they “define” a single point.  If there are two planes in space, and they intersect, what do they define?  (Look at the walls of your room, where they meet. Imagine if there were no floor or ceiling, and the walls went up and down and side to side forever, what would the corner where they meet look like?)
A-a ray
B-a line
C-a point
D-a plane
E-a partridge
F-a pear tree

#4- I choose (D)

4. What is the difference between a plane and a piece of paper?
A- Nothing, both can have lines and points on them
B-You can draw on paper not on a plane
C-You can make a piece of paper into a plane if you know how to fold it
D-A plane is two dimensional and goes on infinitely, a piece of paper has three dimensions and has definite boundaries
E- Nothing, because they are the same thing
F- Planes are used in mathematics, paper is not

#5- I choose (A)

5. I have ry_AY and ry_XZ.  Given only what you've been told, is it possible that they could define an angle?

A-No, because they do not have a common endpoint
B-Yes, because it takes two rays to make an angle
C-No, because there should be a line there
D-Yes, because Y is close to Z in the alphabet
E-No, because ry_AY is very long
F-Yes, if they are on the same plane

#11- I choose (D)

11. Does every ray contain a line segment?
A-Only if there are three points on the ray
B-Yes, because all you need for a line segment is one point
C-No, because an element can't be two things
D-No, because the end point is really an arrow
E-Yes, because every ray needs two points to define it
F-No because the points are busy making a ray

#12- I choose (D)

12. How many points are on a line?
A- None
B-Lots, because lines are infinite
C-2
D-We only need two points to define a line, but a line contains an infinite number of points
E-5 or 6 depending on how long the line is
F-At least 10

13- I choose (E)

13. Does every line contain a ray?
A- Yes, because a ray and a line both have arrows.
B-No, because the two points necessary for a ray are making a line.
C-Yes, because a ray needs two points to exist, which are always part of a line.
D-Sometimes, if the arrows are in the right places
E- No, because lines don't end and a ray needs an endpoint
F- Only if the line has three points on it

#16- I choose (E)

16. If I have two rays, do I have a plane?

A-No, because a ray can't be used to define a plane
B-Yes, because we need three points
C-No, because two rays might only make one line
D-Yes, because rays can be extended into lines, and two would make a plane
E-No, because there aren't enough points
F-Yes, because it's the number of points that matter

#17- I choose (C)

17. If I have an angle, do I have a plane?
A-Only if you have an additional point not on the angle
B-Yes, because any two rays can define a plane
C-No, because there aren't enough points
D-Yes, because angles are big
E- No because rays cannot be extended into lines
F-Yes, because that means you have two lines that meet at a single point

#20- I choose (E)

20. Does every ray eventually create an angle?

A- Only if the ray is also a line.
B-Only if the ray has another point on it
C-Yes, because every ray eventually crosses something
D-No, because a ray can only be a ray
E- No, because a ray only makes an angle at the endpoint
F-No, because it may never cross another line


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#16 2012-08-30 16:04:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,718

Re: Naming Geometry Elements

Hi zee-f;

These are my answers but I am the worst in the world with definitions.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#17 2012-08-30 19:02:46

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,122

Re: Naming Geometry Elements

Hi zee-f

I agree with your answers to 4 and 12.

5. I have ry_AY and ry_XZ.

??? What does this mean, please ?  I don't understand the notation.

I am interested in your on-line course.  Someone else who posts here is also doing the same questions as you. Please would you post a link to the course site.

These questions depend on how the terms are defined.  It is tempting to use my 'common sense' about what these mean but that may lead to wrong answers.

How is the term 'ray' defined?

And 'line' ?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#18 2012-08-31 01:59:39

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

oooh yeah I forgot to mention that point sense am taking an online course

(AB) are examples

A line segment is writin like this : ls_AB 
ls_(then the points am talking about)

line: ln_AB

Ray: ry_AB

angel <BAC


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#19 2012-08-31 02:01:06

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

oooh and I cant really give the course link because you need to have a user name and password to enter the course here is the original website:

www.compuhigh.com


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#20 2012-08-31 02:07:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,718

Re: Naming Geometry Elements

Hi;

How did I do? I had to do a lot of guessing. But as Obi Wan Kenobi says,"trust the force Luke."


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#21 2012-08-31 06:14:58

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

Hi Bobbym,

I still didn’t submit the lesson to see the correct answers. But, I do agree with you on #2. But for #20 a ray begins at a particle point which is called the end point and goes on forever and an angle has two rays that have the same ((end point))
So doesn’t the ray only make an angle at the endpoint?


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#22 2012-08-31 09:06:49

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,122

Re: Naming Geometry Elements

hi zee-f

Thanks for the link.  I thought it would need a password; after all, they are selling this set of courses.  But it was useful to look at the sample lessons. 

Couldn't get to a sample on geometry so I looked up the definitions on Mathswords.com.  (I have never used the term 'ray' before in geometry)

#2- I choose (A)

2. Two points define a line, but if there are two lines in a plane, and if they intersect somewhere, they “define” a single point.  If there are two planes in space, and they intersect, what do they define?  (Look at the walls of your room, where they meet. Imagine if there were no floor or ceiling, and the walls went up and down and side to side forever, what would the corner where they meet look like?)
A-a ray
B-a line
C-a point
D-a plane
E-a partridge
F-a pear tree

As the question says the planes go on forever, I think this should be B- a line   

#4- I choose (D)

4. What is the difference between a plane and a piece of paper?
A- Nothing, both can have lines and points on them
B-You can draw on paper not on a plane
C-You can make a piece of paper into a plane if you know how to fold it
D-A plane is two dimensional and goes on infinitely, a piece of paper has three dimensions and has definite boundaries
E- Nothing, because they are the same thing
F- Planes are used in mathematics, paper is not

I like your answer.  smile 

#5- I choose (A)

5. I have ry_AY and ry_XZ.  Given only what you've been told, is it possible that they could define an angle?

A-No, because they do not have a common endpoint
B-Yes, because it takes two rays to make an angle
C-No, because there should be a line there
D-Yes, because Y is close to Z in the alphabet
E-No, because ry_AY is very long
F-Yes, if they are on the same plane

  I like your answer smile

#11- I choose (D)

11. Does every ray contain a line segment?
A-Only if there are three points on the ray
B-Yes, because all you need for a line segment is one point
C-No, because an element can't be two things
D-No, because the end point is really an arrow
E-Yes, because every ray needs two points to define it
F-No because the points are busy making a ray

If a line segment means a part of an infinite line defined by two end points, then I think this should be E. 

#12- I choose (D)

12. How many points are on a line?
A- None
B-Lots, because lines are infinite
C-2
D-We only need two points to define a line, but a line contains an infinite number of points
E-5 or 6 depending on how long the line is
F-At least 10

Answer D is good! 

13- I choose (E)

13. Does every line contain a ray?
A- Yes, because a ray and a line both have arrows.
B-No, because the two points necessary for a ray are making a line.
C-Yes, because a ray needs two points to exist, which are always part of a line.
D-Sometimes, if the arrows are in the right places
E- No, because lines don't end and a ray needs an endpoint
F- Only if the line has three points on it

  Choose a point on the line to be the end of the ray and then it would appear to be C

#16- I choose (E)

16. If I have two rays, do I have a plane?

A-No, because a ray can't be used to define a plane
B-Yes, because we need three points
C-No, because two rays might only make one line
D-Yes, because rays can be extended into lines, and two would make a plane
E-No, because there aren't enough points
F-Yes, because it's the number of points that matter

If a point has a ray going from it in one direction, and another ray going from it in the opposite direction, then all you have is a line.  So answer C looks right to me. 

#17- I choose (C)

17. If I have an angle, do I have a plane?
A-Only if you have an additional point not on the angle
B-Yes, because any two rays can define a plane
C-No, because there aren't enough points
D-Yes, because angles are big
E- No because rays cannot be extended into lines
F-Yes, because that means you have two lines that meet at a single point

An angle is made from two rays from a single point.  Take a second point on one ray and a third point on the other ray and you have three points (not in a line) so you do have a plane. 

#20- I choose (E)

20. Does every ray eventually create an angle?

A- Only if the ray is also a line.
B-Only if the ray has another point on it
C-Yes, because every ray eventually crosses something
D-No, because a ray can only be a ray
E- No, because a ray only makes an angle at the endpoint
F-No, because it may never cross another line

If you only have this ray then it, on its own, does not make a angle.  So maybe D, but I think I choose answer F

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#23 2012-08-31 09:33:32

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

I would choose B for #17.
I really like the way you explained why you choose the answer it really helped me know more about what a plane is.


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#24 2012-08-31 09:43:47

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Naming Geometry Elements

Here is the rest of my answers:

#1- C

1. We need two points to define a line.  A different way to say this is that if you have two points, you will need at least a line to hold them.  In this sense, what do you need at least three points to define?

A- three lines
Ba ray
Can angle or a plane
Da line or an angle
E a line segment
F a point

3.E
3. In the figure below(IMG), compare the two rays ry_AB and ry_CD.  Which one is longer?

A- ry_CD
B-ry_AB
C-ry_CD because the arrow goes right
D-ry_CD because the points are further apart
E- all rays are the same infinite length
F-ry_AB we just can't see it all


#6- F

6. Consider two lines that intersect in a single point in a plane.  How many rays would it take to draw the same picture?
A-3
B-5
C-1
D-2
E-6
F-4

#9- A

9. Plane geometry as we study it now can be traced back to Euclid, and his book The Elements.  Go HERE (http://www.greenlion.com/Eu-I-1-7.pdf ) to find out more about that book, and find out what it means when they say "A point is that which has no part."  Which of these best sums up that idea:

A-A point has no dimensions, it only defines a place in space
B-Points are only on lines, never by themselves
C-A point is only important if it defines a shape
D-Points are very big
E-Points are very small
F-Points stand alone and have nothing more to them

#10- C

10. Imagine you printed out figure 1 and enlarged it with a photocopier, then compared the two figures.  Everything would appear larger.  Would point B really be larger?

A-Yes, it would become a planet
B-No, because the line it is on would not be bigger
C-Yes, because everything would be bigger
D-No, because a point has no dimensions to enlarge
E-Yes, because point B is on a line segment
F-No, because I think the answer choice should be F

#18- D

18. If I have a line, do I have a plane?

A. Only if you have an additional point not on the line
B.Only if it is a long line
C.Yes, because lines are big
D.Yes, because a line has an infinite number of points
E.Only if the line has three points on it
F Only if the line has 6 or more points on it

19-A

19.If I have three points, do I always have a plane?

A-Yes, because three points are enough
B-Yes, because planes are infinite
C-Only if the points are on the same line
D-No, because all the points may be on the same line
E-No, you might have an angle
F- No, you might have a triangle

View Image: prob3.JPG

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#25 2012-08-31 09:57:49

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,122

Re: Naming Geometry Elements

Yes B is good for 17.

Give me 10 minutes and I'll post back what I think of your other answers.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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