Question

Your friend draws a square and one diagonal connecting it's opposite vertices. Your friend believes that the diagonal is the same length as one side of the square. Do you agree? Explain your reasoning.

Answer 1

Hi,

The answer is No.
Here is the explanation on example.

$s = 5 \\ d = \sqrt{s} = 2.23$

So you can see that s(side) is not equal to d(diagonal)

Hope this helps.
r3t40

Answer 2

Let, Length of Side of a Square=a unit

Since each Interior angle of Square measures 90°.

Length of Diagonal of Square,with the Help of Pythagorean Theorem

                 $=\sqrt{a^2+a^2}\\\\=\sqrt{2a^2}\\\\=\sqrt{2} a$    

Length of Diagonal =√2 a Unit

So,→ Length of Side of Square≠ Length of Diagonal  

No, My friend is incorrect.