How angles opposite to the sides of an equiangular triangle influence the similarity of these sides?

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I hope that the sides opposite to the angles of an equiangular triangle are called homologous sides because these sides are similar.

I would like to know why angles opposite to the sides of an equiangular triangle influence the similarity of these sides. This question developed from this discussion.

triangle

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edited Jul 18 at 21:17

Bernard

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asked Jul 18 at 21:14

justin

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up vote
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I hope that the sides opposite to the angles of an equiangular triangle are called homologous sides because these sides are similar.

I would like to know why angles opposite to the sides of an equiangular triangle influence the similarity of these sides. This question developed from this discussion.

triangle

share|cite|improve this question

edited Jul 18 at 21:17

Bernard

110k635103

asked Jul 18 at 21:14

justin

217113

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I hope that the sides opposite to the angles of an equiangular triangle are called homologous sides because these sides are similar.

I would like to know why angles opposite to the sides of an equiangular triangle influence the similarity of these sides. This question developed from this discussion.

triangle

share|cite|improve this question

edited Jul 18 at 21:17

Bernard

110k635103

asked Jul 18 at 21:14

justin

217113

I hope that the sides opposite to the angles of an equiangular triangle are called homologous sides because these sides are similar.

I would like to know why angles opposite to the sides of an equiangular triangle influence the similarity of these sides. This question developed from this discussion.

triangle

share|cite|improve this question

edited Jul 18 at 21:17

Bernard

110k635103

asked Jul 18 at 21:14

justin

217113

share|cite|improve this question

share|cite|improve this question

edited Jul 18 at 21:17

Bernard

110k635103

edited Jul 18 at 21:17

Bernard

110k635103

edited Jul 18 at 21:17

Bernard

110k635103

110k635103

asked Jul 18 at 21:14

justin

217113

asked Jul 18 at 21:14

justin

217113

asked Jul 18 at 21:14

justin

217113

217113

add a comment | 

add a comment | 

2 Answers
2

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0
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If the triangle is equiangular, it is automatically equilateral. Just stop and think; you have three equal angles and you try to form a triangle with them. You cannot stretch nor elongate the sides,otherwise the angles are going to change ; it is perfectly symmetrical.

share|cite|improve this answer

edited Jul 18 at 21:25

abiessu

6,61721540

answered Jul 18 at 21:24

Elizabeth Middleford

144

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm asking about a case where there are two equiangular triangles. Even though they might be equilateral, they might not be mutually equilateral. In other words, they might be similar if not isometric.
  – justin
  Jul 18 at 21:47
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Well, if you want to know why in similar triangles the ratio of any two sides between them would be in proportion, it is because given two similar equilateral triangles, the ratio of either side of the first and either side of the second is the ratio of similarity, given the fact that the sides are the same for each of the figures. The case of isometric triangles is just one particular case. By the way, the geometric transformations that preserve angles of this form are reflection, rotation, translation and homotetia.
  – Elizabeth Middleford
  Jul 18 at 22:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm looking for an answer regarding the position of angles in two equiangular triangles with it's sides. How does the opposite angles to a given side in these triangles influence the similarity in these equiangular triangles. To be honest I'm not looking for isometric triangles even though isometric triangles are a case of equiangular triangles as you said.
  – justin
  Jul 23 at 21:20
  
  

  
  
  
  

add a comment | 

up vote
0
down vote

If two triangles have the same corner angles, then those are moved, rotated and/or scaled copies.

--- rk

share|cite|improve this answer

answered Jul 18 at 21:28

Dr. Richard Klitzing

7586

add a comment | 

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote

If the triangle is equiangular, it is automatically equilateral. Just stop and think; you have three equal angles and you try to form a triangle with them. You cannot stretch nor elongate the sides,otherwise the angles are going to change ; it is perfectly symmetrical.

share|cite|improve this answer

edited Jul 18 at 21:25

abiessu

6,61721540

answered Jul 18 at 21:24

Elizabeth Middleford

144

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm asking about a case where there are two equiangular triangles. Even though they might be equilateral, they might not be mutually equilateral. In other words, they might be similar if not isometric.
  – justin
  Jul 18 at 21:47
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Well, if you want to know why in similar triangles the ratio of any two sides between them would be in proportion, it is because given two similar equilateral triangles, the ratio of either side of the first and either side of the second is the ratio of similarity, given the fact that the sides are the same for each of the figures. The case of isometric triangles is just one particular case. By the way, the geometric transformations that preserve angles of this form are reflection, rotation, translation and homotetia.
  – Elizabeth Middleford
  Jul 18 at 22:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm looking for an answer regarding the position of angles in two equiangular triangles with it's sides. How does the opposite angles to a given side in these triangles influence the similarity in these equiangular triangles. To be honest I'm not looking for isometric triangles even though isometric triangles are a case of equiangular triangles as you said.
  – justin
  Jul 23 at 21:20
  
  

  
  
  
  

add a comment | 

up vote
0
down vote

If the triangle is equiangular, it is automatically equilateral. Just stop and think; you have three equal angles and you try to form a triangle with them. You cannot stretch nor elongate the sides,otherwise the angles are going to change ; it is perfectly symmetrical.

share|cite|improve this answer

edited Jul 18 at 21:25

abiessu

6,61721540

answered Jul 18 at 21:24

Elizabeth Middleford

144

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm asking about a case where there are two equiangular triangles. Even though they might be equilateral, they might not be mutually equilateral. In other words, they might be similar if not isometric.
  – justin
  Jul 18 at 21:47
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Well, if you want to know why in similar triangles the ratio of any two sides between them would be in proportion, it is because given two similar equilateral triangles, the ratio of either side of the first and either side of the second is the ratio of similarity, given the fact that the sides are the same for each of the figures. The case of isometric triangles is just one particular case. By the way, the geometric transformations that preserve angles of this form are reflection, rotation, translation and homotetia.
  – Elizabeth Middleford
  Jul 18 at 22:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm looking for an answer regarding the position of angles in two equiangular triangles with it's sides. How does the opposite angles to a given side in these triangles influence the similarity in these equiangular triangles. To be honest I'm not looking for isometric triangles even though isometric triangles are a case of equiangular triangles as you said.
  – justin
  Jul 23 at 21:20
  
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

If the triangle is equiangular, it is automatically equilateral. Just stop and think; you have three equal angles and you try to form a triangle with them. You cannot stretch nor elongate the sides,otherwise the angles are going to change ; it is perfectly symmetrical.

share|cite|improve this answer

edited Jul 18 at 21:25

abiessu

6,61721540

answered Jul 18 at 21:24

Elizabeth Middleford

144

If the triangle is equiangular, it is automatically equilateral. Just stop and think; you have three equal angles and you try to form a triangle with them. You cannot stretch nor elongate the sides,otherwise the angles are going to change ; it is perfectly symmetrical.

share|cite|improve this answer

edited Jul 18 at 21:25

abiessu

6,61721540

answered Jul 18 at 21:24

Elizabeth Middleford

144

share|cite|improve this answer

share|cite|improve this answer

edited Jul 18 at 21:25

abiessu

6,61721540

edited Jul 18 at 21:25

abiessu

6,61721540

edited Jul 18 at 21:25

abiessu

6,61721540

6,61721540

answered Jul 18 at 21:24

Elizabeth Middleford

144

answered Jul 18 at 21:24

Elizabeth Middleford

144

answered Jul 18 at 21:24

Elizabeth Middleford

144

144

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm asking about a case where there are two equiangular triangles. Even though they might be equilateral, they might not be mutually equilateral. In other words, they might be similar if not isometric.
  – justin
  Jul 18 at 21:47
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Well, if you want to know why in similar triangles the ratio of any two sides between them would be in proportion, it is because given two similar equilateral triangles, the ratio of either side of the first and either side of the second is the ratio of similarity, given the fact that the sides are the same for each of the figures. The case of isometric triangles is just one particular case. By the way, the geometric transformations that preserve angles of this form are reflection, rotation, translation and homotetia.
  – Elizabeth Middleford
  Jul 18 at 22:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm looking for an answer regarding the position of angles in two equiangular triangles with it's sides. How does the opposite angles to a given side in these triangles influence the similarity in these equiangular triangles. To be honest I'm not looking for isometric triangles even though isometric triangles are a case of equiangular triangles as you said.
  – justin
  Jul 23 at 21:20
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm asking about a case where there are two equiangular triangles. Even though they might be equilateral, they might not be mutually equilateral. In other words, they might be similar if not isometric.
  – justin
  Jul 18 at 21:47
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Well, if you want to know why in similar triangles the ratio of any two sides between them would be in proportion, it is because given two similar equilateral triangles, the ratio of either side of the first and either side of the second is the ratio of similarity, given the fact that the sides are the same for each of the figures. The case of isometric triangles is just one particular case. By the way, the geometric transformations that preserve angles of this form are reflection, rotation, translation and homotetia.
  – Elizabeth Middleford
  Jul 18 at 22:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm looking for an answer regarding the position of angles in two equiangular triangles with it's sides. How does the opposite angles to a given side in these triangles influence the similarity in these equiangular triangles. To be honest I'm not looking for isometric triangles even though isometric triangles are a case of equiangular triangles as you said.
  – justin
  Jul 23 at 21:20
  
  

  
  
  
  

I'm asking about a case where there are two equiangular triangles. Even though they might be equilateral, they might not be mutually equilateral. In other words, they might be similar if not isometric.
– justin
Jul 18 at 21:47

I'm asking about a case where there are two equiangular triangles. Even though they might be equilateral, they might not be mutually equilateral. In other words, they might be similar if not isometric.
– justin
Jul 18 at 21:47

Well, if you want to know why in similar triangles the ratio of any two sides between them would be in proportion, it is because given two similar equilateral triangles, the ratio of either side of the first and either side of the second is the ratio of similarity, given the fact that the sides are the same for each of the figures. The case of isometric triangles is just one particular case. By the way, the geometric transformations that preserve angles of this form are reflection, rotation, translation and homotetia.
– Elizabeth Middleford
Jul 18 at 22:33

Well, if you want to know why in similar triangles the ratio of any two sides between them would be in proportion, it is because given two similar equilateral triangles, the ratio of either side of the first and either side of the second is the ratio of similarity, given the fact that the sides are the same for each of the figures. The case of isometric triangles is just one particular case. By the way, the geometric transformations that preserve angles of this form are reflection, rotation, translation and homotetia.
– Elizabeth Middleford
Jul 18 at 22:33

I'm looking for an answer regarding the position of angles in two equiangular triangles with it's sides. How does the opposite angles to a given side in these triangles influence the similarity in these equiangular triangles. To be honest I'm not looking for isometric triangles even though isometric triangles are a case of equiangular triangles as you said.
– justin
Jul 23 at 21:20

I'm looking for an answer regarding the position of angles in two equiangular triangles with it's sides. How does the opposite angles to a given side in these triangles influence the similarity in these equiangular triangles. To be honest I'm not looking for isometric triangles even though isometric triangles are a case of equiangular triangles as you said.
– justin
Jul 23 at 21:20

add a comment | 

up vote
0
down vote

If two triangles have the same corner angles, then those are moved, rotated and/or scaled copies.

--- rk

share|cite|improve this answer

answered Jul 18 at 21:28

Dr. Richard Klitzing

7586

add a comment | 

up vote
0
down vote

If two triangles have the same corner angles, then those are moved, rotated and/or scaled copies.

--- rk

share|cite|improve this answer

answered Jul 18 at 21:28

Dr. Richard Klitzing

7586

add a comment | 

up vote
0
down vote

up vote
0
down vote

If two triangles have the same corner angles, then those are moved, rotated and/or scaled copies.

--- rk

share|cite|improve this answer

answered Jul 18 at 21:28

Dr. Richard Klitzing

7586

If two triangles have the same corner angles, then those are moved, rotated and/or scaled copies.

--- rk

share|cite|improve this answer

answered Jul 18 at 21:28

Dr. Richard Klitzing

7586

share|cite|improve this answer

share|cite|improve this answer

answered Jul 18 at 21:28

Dr. Richard Klitzing

7586

answered Jul 18 at 21:28

Dr. Richard Klitzing

7586

answered Jul 18 at 21:28

Dr. Richard Klitzing

7586

7586

add a comment | 

add a comment | 

 

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