Triangle altitude's concurrency by symmetry

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Homework Help Overview

The discussion revolves around the proof of concurrency of triangle altitudes, specifically focusing on the equation of altitude AD and the concept of symmetry in deriving equations for other altitudes.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of symmetry in the context of altitude equations, questioning the original poster's terminology and the completeness of the problem statement. There is a focus on understanding the mathematical expression provided and its implications.

Discussion Status

Some participants have offered clarifications regarding the terminology used, suggesting that "symmetry" may not be the appropriate term. The discussion is ongoing, with participants awaiting further input from the original poster to clarify the context and details of the triangle.

Contextual Notes

There are indications that the problem statement may be incomplete, as participants question the definitions of variables and the specifics of the triangle in question. The original poster has provided a diagram, but further details about the triangle's properties remain unspecified.

alijan kk
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Homework Statement


in the proof of triangle altitudes concurrency , i have found the equation of the Altitude AD,
x(x2-x3)+y(y2-y3)-x1(x2-x3)-y1(y2-y3)
triangle.PNG

Homework Equations

The Attempt at a Solution


In the book other altitude equations are written by symmetry,

how is the idea of symmetry is used here ? , .
 

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The first thing you must learn is to be more careful. The problem statement looks incomplete. What is D, x, y, x1, x2, x3, y1, y2, y3?

Did the book say "symmetry"? I don't see any symmetry, but you may have left out some important parts of the problem statement. Otherwise, "symmetry" is probably the wrong word to use. A better word might be "similarly".
 
FactChecker said:
The first thing you must learn is to be more careful. The problem statement looks incomplete. What is D, x, y, x1, x2, x3, y1, y2, y3?

Did the book say "symmetry"? I don't see any symmetry, but you may have left out some important parts of the problem statement. Otherwise, "symmetry" is probably the wrong word to use. A better word might be "similarly".

i have now uploaded the image of triangle ,
 
alijan kk said:

Homework Statement


in the proof of triangle altitudes concurrency , i have found the equation of the Altitude AD,
x(x2-x3)+y(y2-y3)-x1(x2-x3)-y1(y2-y3)
View attachment 219067

Homework Equations

The Attempt at a Solution


In the book other altitude equations are written by symmetry,

how is the idea of symmetry is used here ? , .

x(x2-x3)+y(y2-y3)-x1(x2-x3)-y1(y2-y3)

is a mathematical expression, not an equation. It has no equal sign.

Did you mean to set this expression equal to zero ?
 
The diagram I see now is better. Did the book say anything else about the triangle? Is it equilateral or isosceles?
 
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@alijan kk: As others have pointed out, it isn't "symmetry", but here is what your author is using. In your figure, if you rotate the labels counterclockwise you will have replaced the subscripts 1 by 2, 2 by 3, and 3 by 1.Then the same steps on the points A, B, and C that were used to get your original expression will give an answer you can get by replacing 1 by 2, 2 by 3, and 3 by 1 in your original expression. Then rotate the subscripts one more time for the third equation. (It has already been pointed out to you that you haven't written equations).
 
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At this point, I think we need to wait for OP to return to this thread.
 
LCKurtz said:
@alijan kk: As others have pointed out, it isn't "symmetry", but here is what your author is using. In your figure, if you rotate the labels counterclockwise you will have replaced the subscripts 1 by 2, 2 by 3, and 3 by 1.Then the same steps on the points A, B, and C that were used to get your original expression will give an answer you can get by replacing 1 by 2, 2 by 3, and 3 by 1 in your original expression. Then rotate the subscripts one more time for the third equation. (It has already been pointed out to you that you haven't written equations).
VERY HELPFULL <3 yes I would take care of the description next time
 
FactChecker said:
The diagram I see now is better. Did the book say anything else about the triangle? Is it equilateral or isosceles?
No just a triangle to proov triangle alititudes concurrency
 

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