# A Triangle-Square

1. May 26, 2013

### adjacent

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)

#### Attached Files:

• ###### Square-Triangle.png
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1.6 KB
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66
Last edited: May 26, 2013
2. May 26, 2013

### Vorde

Is this a homework question? And if not, an you show us or explain to us what you tried?

3. May 26, 2013

### Number Nine

I'm not convinced that this is true. Why doesn't my counterexample work?

#### Attached Files:

• ###### counterexample.png
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4. May 26, 2013

### phinds

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?

5. May 26, 2013

### Vorde

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.

6. May 26, 2013

### Number Nine

It would almost certainly be true in that case. I would accept a handwavy proof by symmetry.

7. May 27, 2013

### adjacent

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.

8. May 27, 2013

### phinds

What do you mean "touch a side"? It's not clear what configuration you mean. Draw an example

9. May 27, 2013

### Number Nine

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.

#### Attached Files:

• ###### counterexample.png
File size:
1.2 KB
Views:
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10. May 28, 2013

### adjacent

You are right Number nine,Thanks!

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