Proving X, A, and Y Lie in a Straight Line | Triangle Medians Proof

  • Thread starter Jarvis Bull Dawg
  • Start date
In summary, "Reductio ad Absurdium" is a form of logical argumentation that aims to disprove a statement or belief by showing that it leads to absurd or contradictory conclusions. It works by assuming the statement is true and using logical reasoning to demonstrate that this leads to absurd results. The purpose of using this type of argument is to expose flaws and encourage critical thinking. Examples of "Reductio ad Absurdium" include proving the irrationality of the square root of 2 and there are limitations to its use as the sole basis for disproving a statement.
  • #1
Jarvis Bull Dawg
17
0
This is question I am really stuck with, please help if you can. (Its by indirect proof).
Question: The medians BD and CE in triangle ABC are produced to X and Y respectively so that BD = DX and CE = EY. Prove that X, A, and Y lie in a straight line.
 
Last edited:
Physics news on Phys.org
  • #2
Here is what I have so far:
 

Attachments

  • Diagram1.GIF
    Diagram1.GIF
    1 KB · Views: 499
Last edited:
  • #3
No need in absurdum!

Connect C and X and see what helpful figure you are getting.
Same for B and Y.
Precise drawing would help.
 

Related to Proving X, A, and Y Lie in a Straight Line | Triangle Medians Proof

What is "Reductio ad Absurdium"?

"Reductio ad Absurdium" is a form of logical argumentation that aims to disprove a statement or belief by showing that it leads to absurd or contradictory conclusions.

How does "Reductio ad Absurdium" work?

In this form of argumentation, a person starts by assuming that a statement or belief is true. They then use logical reasoning to show that if the statement is true, it leads to absurd or contradictory results. This demonstrates that the original statement cannot be true.

What is the purpose of using "Reductio ad Absurdium"?

The purpose of using this type of argument is to expose the flaws or contradictions in a statement or belief. It can be used to challenge the validity of an argument and encourage critical thinking and logical reasoning.

What are some examples of "Reductio ad Absurdium"?

A classic example of "Reductio ad Absurdium" is the proof that the square root of 2 is an irrational number. By assuming the opposite, that the square root of 2 is a rational number, and using logical reasoning, one can show that this leads to absurd results, such as contradicting the fundamental laws of mathematics.

Are there any limitations to using "Reductio ad Absurdium"?

While "Reductio ad Absurdium" can be a powerful tool in exposing flaws in an argument, it should not be used as the sole basis for disproving a statement or belief. It is important to also consider other evidence and logical reasoning in forming a conclusion.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
17
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
12
Views
2K
Replies
1
Views
854
  • Precalculus Mathematics Homework Help
Replies
15
Views
4K
  • Precalculus Mathematics Homework Help
Replies
3
Views
2K
  • Precalculus Mathematics Homework Help
Replies
11
Views
8K
Back
Top