Fdtxjr

Has any country ever had 2 former presidents in jail simultaneously?

Is there a name for this algorithm to calculate the concentration of a mixture of two solutions containing the same solute?

Where does the bonus feat in the cleric starting package come from?

What are the purposes of autoencoders?

C++ debug/print custom type with GDB : the case of nlohmann json library

If a character has darkvision, can they see through an area of nonmagical darkness filled with lightly obscuring gas?

How do I color the graph in datavisualization?

How to implement a feedback to keep the DC gain at zero for this conceptual passive filter?

Aragorn's "guise" in the Orthanc Stone

On a tidally locked planet, would time be quantized?

Problem with TransformedDistribution

How do you make your own symbol when Detexify fails?

Are the IPv6 address space and IPv4 address space completely disjoint?

Travelling outside the UK without a passport

why `nmap 192.168.1.97` returns less services than `nmap 127.0.0.1`?

How much character growth crosses the line into breaking the character

Why does the Sun have different day lengths, but not the gas giants?

WiFi Thermostat, No C Terminal on Furnace

What prevents the use of a multi-segment ILS for non-straight approaches?

Non-trope happy ending?

Which one is correct as adjective “protruding” or “protruded”?

Intuition of generalized eigenvector.

"Spoil" vs "Ruin"

Does an advisor owe his/her student anything? Will an advisor keep a PhD student only out of pity?

If a ray r emanating from an exterior point of triangle ABC intersects side AB at any point between A and B, then r also intersects side AC or side BC [duplicate]

Justify each step in the following proof of Proposition 3.9 (a). I like to know if I'm in the right track and I'm also missing a few of themGiven triangle ABC, if D is an interior pt and E is an exterior pt, segment DE intersects triangle ABC?Finding the Perimiter of a right Triangle given an interior angle bisector and exterior angle bisectorQuestion about proof regarding a triangle and a line.Given a point origin, find ray that intersects two linesProve In Equilateral Triangle $ABC$ $AM$ and $AN$ are equalProve that ray CE intersects $triangle ABC$ at a point $D$ on $AB$ and that $D$ must lie strictly between $A$ and $B$.Justify each step in the following proof of Proposition 3.9 (a). I like to know if I'm in the right track and I'm also missing a few of themGeometry: Construct a rectangle with area equal to a given triangle and with one side equal to a given segment.Given a triangle $ABC$, make it a point $D$ on the side $AB$.Prove that if a ray has its endpoint on a line, where the ray is not on the line, then the points of the ray are on the same side of the line.

1

$begingroup$

This question is an exact duplicate of:

• 
  Justify each step in the following proof of Proposition 3.9 (a). I like to know if I'm in the right track and I'm also missing a few of them
  
  1 answer
  
  

Prove Proposition 3.9:
If a ray r emanating from an exterior point of triangle $ABC$ intersects side $AB$ at any point between $A$ and $B$, then $r$ also intersects side $AC$ or side $BC$.

Can someone help me finish this proof I started

By the hypothesis, let $DE$ be a ray emanating from an exterior point $D$ of triangle $ABC$ where the ray $DE$ intersects $AB$ at point $E$ such that $A*E*B$.

By pachs theorem, the line DE either intersects $AC$ or $BC$.
3.Suppose $DE$ intersects $AC$ at point $M$ where $M$ is not equal to $A$
Then by the definition of line segment, either $M=C$, or $D*M*E$

geometry euclidean-geometry education math-history

share|cite|improve this question

edited Mar 15 at 17:45

Math1234

asked Mar 15 at 17:05

Math1234Math1234

63

$endgroup$

marked as duplicate by Lee David Chung Lin, Leucippus, Lord Shark the Unknown, Vinyl_cape_jawa, uniquesolution Mar 16 at 9:57

This question was marked as an exact duplicate of an existing question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Please change the title of your question - proposition 3.9a is not something people will know.
  $endgroup$
  – Piotr Benedysiuk
  Mar 15 at 17:18
  

  
  
  
  

add a comment | 

1

$begingroup$

This question is an exact duplicate of:

• 
  Justify each step in the following proof of Proposition 3.9 (a). I like to know if I'm in the right track and I'm also missing a few of them
  
  1 answer
  
  

Prove Proposition 3.9:
If a ray r emanating from an exterior point of triangle $ABC$ intersects side $AB$ at any point between $A$ and $B$, then $r$ also intersects side $AC$ or side $BC$.

Can someone help me finish this proof I started

By the hypothesis, let $DE$ be a ray emanating from an exterior point $D$ of triangle $ABC$ where the ray $DE$ intersects $AB$ at point $E$ such that $A*E*B$.

By pachs theorem, the line DE either intersects $AC$ or $BC$.
3.Suppose $DE$ intersects $AC$ at point $M$ where $M$ is not equal to $A$
Then by the definition of line segment, either $M=C$, or $D*M*E$

geometry euclidean-geometry education math-history

share|cite|improve this question

edited Mar 15 at 17:45

Math1234

asked Mar 15 at 17:05

Math1234Math1234

63

$endgroup$

marked as duplicate by Lee David Chung Lin, Leucippus, Lord Shark the Unknown, Vinyl_cape_jawa, uniquesolution Mar 16 at 9:57

This question was marked as an exact duplicate of an existing question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Please change the title of your question - proposition 3.9a is not something people will know.
  $endgroup$
  – Piotr Benedysiuk
  Mar 15 at 17:18
  

  
  
  
  

add a comment | 

$begingroup$

This question is an exact duplicate of:

• 
  Justify each step in the following proof of Proposition 3.9 (a). I like to know if I'm in the right track and I'm also missing a few of them
  
  1 answer
  
  

Prove Proposition 3.9:
If a ray r emanating from an exterior point of triangle $ABC$ intersects side $AB$ at any point between $A$ and $B$, then $r$ also intersects side $AC$ or side $BC$.

Can someone help me finish this proof I started

By the hypothesis, let $DE$ be a ray emanating from an exterior point $D$ of triangle $ABC$ where the ray $DE$ intersects $AB$ at point $E$ such that $A*E*B$.

By pachs theorem, the line DE either intersects $AC$ or $BC$.
3.Suppose $DE$ intersects $AC$ at point $M$ where $M$ is not equal to $A$
Then by the definition of line segment, either $M=C$, or $D*M*E$

geometry euclidean-geometry education math-history

share|cite|improve this question

edited Mar 15 at 17:45

Math1234

asked Mar 15 at 17:05

Math1234Math1234

63

$endgroup$

share|cite|improve this question

edited Mar 15 at 17:45

Math1234

asked Mar 15 at 17:05

Math1234Math1234

63

share|cite|improve this question

edited Mar 15 at 17:45

Math1234

asked Mar 15 at 17:05

Math1234Math1234

63

asked Mar 15 at 17:05

Math1234Math1234

63

asked Mar 15 at 17:05

Math1234Math1234

63

1 Answer
1

active

oldest

votes

0

$begingroup$

Then by the definition of line segment, either $M=C$, or $D*M*E$

This step is not correct/justified.

Up to that point your proof is correct. In fact, the only thing you need to conclude the proof is that $D*E*M$ or $D*M*E$. Since these points are distinct, you may assume the contrary i.e. $E*D*M$, and show that $D$ is an interior point of a triangle which contradicts the assumption. To do this, prove that $D$ belongs to all three halfplanes which determine the interior of a triangle.

share|cite|improve this answer

answered Mar 15 at 19:13

KulistyKulisty

419216

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How exactly would you prove D is in the interior? What would the layout of it be? I'm confused how to show how EDM means that D in the interior.
  $endgroup$
  – Math1234
  Mar 21 at 3:48
  

  
  
  
  

add a comment | 

0

$begingroup$

Then by the definition of line segment, either $M=C$, or $D*M*E$

This step is not correct/justified.

Up to that point your proof is correct. In fact, the only thing you need to conclude the proof is that $D*E*M$ or $D*M*E$. Since these points are distinct, you may assume the contrary i.e. $E*D*M$, and show that $D$ is an interior point of a triangle which contradicts the assumption. To do this, prove that $D$ belongs to all three halfplanes which determine the interior of a triangle.

share|cite|improve this answer

answered Mar 15 at 19:13

KulistyKulisty

419216

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How exactly would you prove D is in the interior? What would the layout of it be? I'm confused how to show how EDM means that D in the interior.
  $endgroup$
  – Math1234
  Mar 21 at 3:48
  

  
  
  
  

add a comment | 

0

$begingroup$

Then by the definition of line segment, either $M=C$, or $D*M*E$

This step is not correct/justified.

Up to that point your proof is correct. In fact, the only thing you need to conclude the proof is that $D*E*M$ or $D*M*E$. Since these points are distinct, you may assume the contrary i.e. $E*D*M$, and show that $D$ is an interior point of a triangle which contradicts the assumption. To do this, prove that $D$ belongs to all three halfplanes which determine the interior of a triangle.

share|cite|improve this answer

answered Mar 15 at 19:13

KulistyKulisty

419216

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How exactly would you prove D is in the interior? What would the layout of it be? I'm confused how to show how EDM means that D in the interior.
  $endgroup$
  – Math1234
  Mar 21 at 3:48
  

  
  
  
  

add a comment | 

$begingroup$

Then by the definition of line segment, either $M=C$, or $D*M*E$

This step is not correct/justified.

Up to that point your proof is correct. In fact, the only thing you need to conclude the proof is that $D*E*M$ or $D*M*E$. Since these points are distinct, you may assume the contrary i.e. $E*D*M$, and show that $D$ is an interior point of a triangle which contradicts the assumption. To do this, prove that $D$ belongs to all three halfplanes which determine the interior of a triangle.

share|cite|improve this answer

answered Mar 15 at 19:13

KulistyKulisty

419216

$endgroup$

share|cite|improve this answer

answered Mar 15 at 19:13

KulistyKulisty

419216

answered Mar 15 at 19:13

KulistyKulisty

419216

answered Mar 15 at 19:13

KulistyKulisty

419216