# A Triangle-Square

Gold Member
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)

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• Square-Triangle.png
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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?

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• counterexample.png
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phinds
Gold Member
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.

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.

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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.

phinds
Gold Member
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

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
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Gold Member
You are right Number nine,Thanks!