Given 3 slopes of 3 lines in which all three wont intersect at the same point. How can we determine whether a triangle can be formed or not? [on hold]

Clash Royale CLAN TAG#URR8PPP

up vote
2
down vote

favorite

For example
The angles made by the $3$ lines are $50$, $90$, $20$ with $x$ axis.
How can we prove mathematically that they can form a triangle?

Actually I'm writing a program that takes n slopes as input and prints the no. of triangles that can be formed with them. so, in a mathematical way I have asked this question.

geometry

share|cite|improve this question

edited Aug 3 at 18:33

asked Aug 2 at 18:35

murthy

112

put on hold as off-topic by amWhy, John Ma, Adrian Keister, Isaac Browne, Taroccoesbrocco Aug 3 at 0:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, John Ma, Adrian Keister, Isaac Browne, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  That's not true in general, if all of the three lines meet at a point they don't form a triangle.
  – Javi
  Aug 2 at 18:42
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  So long as the three slopes differ and the lines don't all meet in a point, then a triangle must be formed. Simple.
  – David G. Stork
  Aug 2 at 18:43
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is not true. the so-called triangle inequality must be fulfilled!
  – Dr. Sonnhard Graubner
  Aug 2 at 19:11
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Can you say what is that triangle inequality?
  – murthy
  Aug 2 at 19:45
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @Dr.SonnhardGraubner: I would really like to see how you involve the triangle inequality here.
  – Martin Argerami
  Aug 2 at 23:54
  

  
  
  
  

add a comment | 

up vote
2
down vote

favorite

For example
The angles made by the $3$ lines are $50$, $90$, $20$ with $x$ axis.
How can we prove mathematically that they can form a triangle?

Actually I'm writing a program that takes n slopes as input and prints the no. of triangles that can be formed with them. so, in a mathematical way I have asked this question.

geometry

share|cite|improve this question

edited Aug 3 at 18:33

asked Aug 2 at 18:35

murthy

112

put on hold as off-topic by amWhy, John Ma, Adrian Keister, Isaac Browne, Taroccoesbrocco Aug 3 at 0:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, John Ma, Adrian Keister, Isaac Browne, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  That's not true in general, if all of the three lines meet at a point they don't form a triangle.
  – Javi
  Aug 2 at 18:42
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  So long as the three slopes differ and the lines don't all meet in a point, then a triangle must be formed. Simple.
  – David G. Stork
  Aug 2 at 18:43
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is not true. the so-called triangle inequality must be fulfilled!
  – Dr. Sonnhard Graubner
  Aug 2 at 19:11
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Can you say what is that triangle inequality?
  – murthy
  Aug 2 at 19:45
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @Dr.SonnhardGraubner: I would really like to see how you involve the triangle inequality here.
  – Martin Argerami
  Aug 2 at 23:54
  

  
  
  
  

add a comment | 

up vote
2
down vote

favorite

up vote
2
down vote

favorite

For example
The angles made by the $3$ lines are $50$, $90$, $20$ with $x$ axis.
How can we prove mathematically that they can form a triangle?

Actually I'm writing a program that takes n slopes as input and prints the no. of triangles that can be formed with them. so, in a mathematical way I have asked this question.

geometry

share|cite|improve this question

edited Aug 3 at 18:33

asked Aug 2 at 18:35

murthy

112

For example
The angles made by the $3$ lines are $50$, $90$, $20$ with $x$ axis.
How can we prove mathematically that they can form a triangle?

Actually I'm writing a program that takes n slopes as input and prints the no. of triangles that can be formed with them. so, in a mathematical way I have asked this question.

geometry

share|cite|improve this question

edited Aug 3 at 18:33

asked Aug 2 at 18:35

murthy

112

share|cite|improve this question

share|cite|improve this question

edited Aug 3 at 18:33

edited Aug 3 at 18:33

edited Aug 3 at 18:33

asked Aug 2 at 18:35

murthy

112

asked Aug 2 at 18:35

murthy

112

asked Aug 2 at 18:35

murthy

112

112

put on hold as off-topic by amWhy, John Ma, Adrian Keister, Isaac Browne, Taroccoesbrocco Aug 3 at 0:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, John Ma, Adrian Keister, Isaac Browne, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by amWhy, John Ma, Adrian Keister, Isaac Browne, Taroccoesbrocco Aug 3 at 0:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, John Ma, Adrian Keister, Isaac Browne, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  That's not true in general, if all of the three lines meet at a point they don't form a triangle.
  – Javi
  Aug 2 at 18:42
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  So long as the three slopes differ and the lines don't all meet in a point, then a triangle must be formed. Simple.
  – David G. Stork
  Aug 2 at 18:43
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is not true. the so-called triangle inequality must be fulfilled!
  – Dr. Sonnhard Graubner
  Aug 2 at 19:11
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Can you say what is that triangle inequality?
  – murthy
  Aug 2 at 19:45
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @Dr.SonnhardGraubner: I would really like to see how you involve the triangle inequality here.
  – Martin Argerami
  Aug 2 at 23:54
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  That's not true in general, if all of the three lines meet at a point they don't form a triangle.
  – Javi
  Aug 2 at 18:42
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  So long as the three slopes differ and the lines don't all meet in a point, then a triangle must be formed. Simple.
  – David G. Stork
  Aug 2 at 18:43
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is not true. the so-called triangle inequality must be fulfilled!
  – Dr. Sonnhard Graubner
  Aug 2 at 19:11
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Can you say what is that triangle inequality?
  – murthy
  Aug 2 at 19:45
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @Dr.SonnhardGraubner: I would really like to see how you involve the triangle inequality here.
  – Martin Argerami
  Aug 2 at 23:54
  

  
  
  
  

3

3

That's not true in general, if all of the three lines meet at a point they don't form a triangle.
– Javi
Aug 2 at 18:42

That's not true in general, if all of the three lines meet at a point they don't form a triangle.
– Javi
Aug 2 at 18:42

2

2

So long as the three slopes differ and the lines don't all meet in a point, then a triangle must be formed. Simple.
– David G. Stork
Aug 2 at 18:43

So long as the three slopes differ and the lines don't all meet in a point, then a triangle must be formed. Simple.
– David G. Stork
Aug 2 at 18:43

This is not true. the so-called triangle inequality must be fulfilled!
– Dr. Sonnhard Graubner
Aug 2 at 19:11

This is not true. the so-called triangle inequality must be fulfilled!
– Dr. Sonnhard Graubner
Aug 2 at 19:11

1

1

Can you say what is that triangle inequality?
– murthy
Aug 2 at 19:45

Can you say what is that triangle inequality?
– murthy
Aug 2 at 19:45

2

2

@Dr.SonnhardGraubner: I would really like to see how you involve the triangle inequality here.
– Martin Argerami
Aug 2 at 23:54

@Dr.SonnhardGraubner: I would really like to see how you involve the triangle inequality here.
– Martin Argerami
Aug 2 at 23:54

add a comment | 

2 Answers
2

active

oldest

votes

up vote
0
down vote

The information about the angles tells us that none of the lines is parallel to another.

It could be the case that the three lines intersect at a single point, and in that case there is no triangle.

If the three lines do not intersect at a point, call the lines $L_1,L_2,L_3$. Let $A$ be the intersection of $L_1$ and $L_2$, and $B$ the intersection of $L_1$ and $L_3$. We cannot have $A=B$ by our assumption. Since $L_2$ and $L_3$ are not parallel, they intersect at a point $C$. We cannot have $C=A$ or $C=B$ because again we would have a triple intersection. So $ABC$ is a triangle formed by the three lines.

share|cite|improve this answer

answered Aug 2 at 23:58

Martin Argerami

115k1071164

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thankyou for helping me.
  – murthy
  Aug 3 at 18:35
  

  
  
  
  

add a comment | 

up vote
0
down vote

This generally depends on the relative position of the lines but if we force two of them intersect at origin the 3rd one shouldn't be concurrent with the two others i.e. if two lines with angles $20$ and $50$ intersect at origin the other one with angle being 90 should be of form$$x=aquad,quad ane 0$$Another way to saying that is: if the slopes are distinct i.e. all three angles are in the interval $left[-dfracpi2,dfracpi2right)$ and distinct, knowing that this lines aren't concurrent they always form a triangle.

share|cite|improve this answer

edited Aug 3 at 7:52

answered Aug 2 at 19:13

Mostafa Ayaz

8,5183630

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please do not take co ordinates into consideration. Please try to make it mathematically prooved only with slopes
  – murthy
  Aug 2 at 19:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Alright! I added some other information. Hope it works...
  – Mostafa Ayaz
  Aug 3 at 7:52
  

  
  
  
  

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote

The information about the angles tells us that none of the lines is parallel to another.

It could be the case that the three lines intersect at a single point, and in that case there is no triangle.

If the three lines do not intersect at a point, call the lines $L_1,L_2,L_3$. Let $A$ be the intersection of $L_1$ and $L_2$, and $B$ the intersection of $L_1$ and $L_3$. We cannot have $A=B$ by our assumption. Since $L_2$ and $L_3$ are not parallel, they intersect at a point $C$. We cannot have $C=A$ or $C=B$ because again we would have a triple intersection. So $ABC$ is a triangle formed by the three lines.

share|cite|improve this answer

answered Aug 2 at 23:58

Martin Argerami

115k1071164

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thankyou for helping me.
  – murthy
  Aug 3 at 18:35
  

  
  
  
  

add a comment | 

up vote
0
down vote

The information about the angles tells us that none of the lines is parallel to another.

It could be the case that the three lines intersect at a single point, and in that case there is no triangle.

If the three lines do not intersect at a point, call the lines $L_1,L_2,L_3$. Let $A$ be the intersection of $L_1$ and $L_2$, and $B$ the intersection of $L_1$ and $L_3$. We cannot have $A=B$ by our assumption. Since $L_2$ and $L_3$ are not parallel, they intersect at a point $C$. We cannot have $C=A$ or $C=B$ because again we would have a triple intersection. So $ABC$ is a triangle formed by the three lines.

share|cite|improve this answer

answered Aug 2 at 23:58

Martin Argerami

115k1071164

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thankyou for helping me.
  – murthy
  Aug 3 at 18:35
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

The information about the angles tells us that none of the lines is parallel to another.

It could be the case that the three lines intersect at a single point, and in that case there is no triangle.

If the three lines do not intersect at a point, call the lines $L_1,L_2,L_3$. Let $A$ be the intersection of $L_1$ and $L_2$, and $B$ the intersection of $L_1$ and $L_3$. We cannot have $A=B$ by our assumption. Since $L_2$ and $L_3$ are not parallel, they intersect at a point $C$. We cannot have $C=A$ or $C=B$ because again we would have a triple intersection. So $ABC$ is a triangle formed by the three lines.

share|cite|improve this answer

answered Aug 2 at 23:58

Martin Argerami

115k1071164

The information about the angles tells us that none of the lines is parallel to another.

It could be the case that the three lines intersect at a single point, and in that case there is no triangle.

If the three lines do not intersect at a point, call the lines $L_1,L_2,L_3$. Let $A$ be the intersection of $L_1$ and $L_2$, and $B$ the intersection of $L_1$ and $L_3$. We cannot have $A=B$ by our assumption. Since $L_2$ and $L_3$ are not parallel, they intersect at a point $C$. We cannot have $C=A$ or $C=B$ because again we would have a triple intersection. So $ABC$ is a triangle formed by the three lines.

share|cite|improve this answer

answered Aug 2 at 23:58

Martin Argerami

115k1071164

share|cite|improve this answer

share|cite|improve this answer

answered Aug 2 at 23:58

Martin Argerami

115k1071164

answered Aug 2 at 23:58

Martin Argerami

115k1071164

answered Aug 2 at 23:58

Martin Argerami

115k1071164

115k1071164

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thankyou for helping me.
  – murthy
  Aug 3 at 18:35
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thankyou for helping me.
  – murthy
  Aug 3 at 18:35
  

  
  
  
  

thankyou for helping me.
– murthy
Aug 3 at 18:35

thankyou for helping me.
– murthy
Aug 3 at 18:35

add a comment | 

up vote
0
down vote

This generally depends on the relative position of the lines but if we force two of them intersect at origin the 3rd one shouldn't be concurrent with the two others i.e. if two lines with angles $20$ and $50$ intersect at origin the other one with angle being 90 should be of form$$x=aquad,quad ane 0$$Another way to saying that is: if the slopes are distinct i.e. all three angles are in the interval $left[-dfracpi2,dfracpi2right)$ and distinct, knowing that this lines aren't concurrent they always form a triangle.

share|cite|improve this answer

edited Aug 3 at 7:52

answered Aug 2 at 19:13

Mostafa Ayaz

8,5183630

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please do not take co ordinates into consideration. Please try to make it mathematically prooved only with slopes
  – murthy
  Aug 2 at 19:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Alright! I added some other information. Hope it works...
  – Mostafa Ayaz
  Aug 3 at 7:52
  

  
  
  
  

add a comment | 

up vote
0
down vote

This generally depends on the relative position of the lines but if we force two of them intersect at origin the 3rd one shouldn't be concurrent with the two others i.e. if two lines with angles $20$ and $50$ intersect at origin the other one with angle being 90 should be of form$$x=aquad,quad ane 0$$Another way to saying that is: if the slopes are distinct i.e. all three angles are in the interval $left[-dfracpi2,dfracpi2right)$ and distinct, knowing that this lines aren't concurrent they always form a triangle.

share|cite|improve this answer

edited Aug 3 at 7:52

answered Aug 2 at 19:13

Mostafa Ayaz

8,5183630

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please do not take co ordinates into consideration. Please try to make it mathematically prooved only with slopes
  – murthy
  Aug 2 at 19:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Alright! I added some other information. Hope it works...
  – Mostafa Ayaz
  Aug 3 at 7:52
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

This generally depends on the relative position of the lines but if we force two of them intersect at origin the 3rd one shouldn't be concurrent with the two others i.e. if two lines with angles $20$ and $50$ intersect at origin the other one with angle being 90 should be of form$$x=aquad,quad ane 0$$Another way to saying that is: if the slopes are distinct i.e. all three angles are in the interval $left[-dfracpi2,dfracpi2right)$ and distinct, knowing that this lines aren't concurrent they always form a triangle.

share|cite|improve this answer

edited Aug 3 at 7:52

answered Aug 2 at 19:13

Mostafa Ayaz

8,5183630

This generally depends on the relative position of the lines but if we force two of them intersect at origin the 3rd one shouldn't be concurrent with the two others i.e. if two lines with angles $20$ and $50$ intersect at origin the other one with angle being 90 should be of form$$x=aquad,quad ane 0$$Another way to saying that is: if the slopes are distinct i.e. all three angles are in the interval $left[-dfracpi2,dfracpi2right)$ and distinct, knowing that this lines aren't concurrent they always form a triangle.

share|cite|improve this answer

edited Aug 3 at 7:52

answered Aug 2 at 19:13

Mostafa Ayaz

8,5183630

share|cite|improve this answer

share|cite|improve this answer

edited Aug 3 at 7:52

edited Aug 3 at 7:52

edited Aug 3 at 7:52

answered Aug 2 at 19:13

Mostafa Ayaz

8,5183630

answered Aug 2 at 19:13

Mostafa Ayaz

8,5183630

answered Aug 2 at 19:13

Mostafa Ayaz

8,5183630

8,5183630

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please do not take co ordinates into consideration. Please try to make it mathematically prooved only with slopes
  – murthy
  Aug 2 at 19:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Alright! I added some other information. Hope it works...
  – Mostafa Ayaz
  Aug 3 at 7:52
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please do not take co ordinates into consideration. Please try to make it mathematically prooved only with slopes
  – murthy
  Aug 2 at 19:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Alright! I added some other information. Hope it works...
  – Mostafa Ayaz
  Aug 3 at 7:52
  

  
  
  
  

Please do not take co ordinates into consideration. Please try to make it mathematically prooved only with slopes
– murthy
Aug 2 at 19:48

Please do not take co ordinates into consideration. Please try to make it mathematically prooved only with slopes
– murthy
Aug 2 at 19:48

Alright! I added some other information. Hope it works...
– Mostafa Ayaz
Aug 3 at 7:52

Alright! I added some other information. Hope it works...
– Mostafa Ayaz
Aug 3 at 7:52

add a comment |