Geometry & Algebra: Proving Triangle-Square

  • Thread starter Thread starter adjacent
  • Start date Start date
AI Thread Summary
The discussion centers on the geometric and algebraic proof that if a square fits perfectly within a triangle, at least two sides of the triangle must be of equal length. Participants express skepticism about the claim, debating the conditions under which the square fits, such as whether it aligns with the midpoint of a triangle's side. Some suggest that a symmetrical arrangement could support the assertion, while others provide counterexamples that challenge its validity. The conversation highlights the need for clarity in the configuration of the square and triangle to understand the relationship between their dimensions. Ultimately, the proof remains unverified, leaving participants seeking further explanation and visual examples.
adjacent
Gold Member
Messages
1,552
Reaction score
62
As you see in the attachment if a square exactly fits in a triangle of any shape,Then atleast Two sides of that triangle would be of equal length(Upper two sides as in attachment)

Explain this Geometrically and algebraically

I tried it but in vain(Im a 9th grader)
 

Attachments

  • Square-Triangle.png
    Square-Triangle.png
    1.7 KB · Views: 493
Last edited:
Mathematics news on Phys.org
Is this a homework question? And if not, an you show us or explain to us what you tried?
 
I'm not convinced that this is true. Why doesn't my counterexample work?
 

Attachments

  • counterexample.png
    counterexample.png
    1,023 bytes · Views: 481
adjacent said:
As you see in the attachment if a square exactly fits in a triangle of any shape,Then atleast Two sides of that triangle would be of equal length(Upper two sides as in attachment)

Explain this Geometrically and algebraically

I tried it but in vain(Im a 9th grader)

Well, see, here's the thing. When you CHOOSE a triangle that has two equal sides, you do indeed get a triangle with 2 equal sides. So what? What about Number Nine's example?
 
My bet is that part of the assignment details that the square has to line up with the midpoint of one of the sides. Then (I think) it would be true.
 
Vorde said:
My bet is that part of the assignment details that the square has to line up with the midpoint of one of the sides. Then (I think) it would be true.

It would almost certainly be true in that case. I would accept a handwavy proof by symmetry.
 
sorry!Only one side of the square should touch a side of the triangle.The other two sides should touch one of the corners of the square.Then this will be correct.This is no homework,I am just curious.I could not find any explanation.
 
adjacent said:
sorry!Only one side of the square should touch a side of the triangle.The other two sides should touch one of the corners of the square.Then this will be correct.This is no homework,I am just curious.I could not find any explanation.

What do you mean "touch a side"? It's not clear what configuration you mean. Draw an example
 
adjacent said:
sorry!Only one side of the square should touch a side of the triangle.The other two sides should touch one of the corners of the square.Then this will be correct.This is no homework,I am just curious.I could not find any explanation.

I'm still not convinced. You could still have a situation like the one illustrated in my picture (attached), and I'm not sure that 2 sides would necessarily be the same length.
 

Attachments

  • counterexample.png
    counterexample.png
    1.2 KB · Views: 494
  • #10
You are right Number nine,Thanks!
 

Similar threads

B Understanding the Pythagorean Theorem
Replies
38
Views
4K
B A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints
Replies
13
Views
2K
MHB Can an Ellipse Help Solve the Scalene Triangle Problem?
Replies
1
Views
1K
MHB Why Can't a Right Triangle Have Sides that Add Up to the Area of Squares?
Replies
2
Views
2K
MHB Distance between points in a triangle
Replies
1
Views
3K
MHB Find side length, cirumference and area of octagon
Replies
3
Views
2K
I Equation for circle points in 3D
Replies
3
Views
3K
MHB Solving the Tangram Puzzle Geometrically (No Constructions)
Replies
6
Views
3K
Find the limit of the sum of the areas of all these triangles
Replies
7
Views
1K
MHB Explaining Dimensions of Tanagrams Without Midpoint Assumptions
Replies
2
Views
5K

Hot Threads

Recent Insights

Back
Top