Hi

Principle 5: The length of a leg opposite a 45 degree angle equals one-half the length of the hypotenuse times the square root of 2.

$\displaystyle a=\tfrac{1}{2}c\sqrt{2}$

why is this so? when I solve for 'a' in $\displaystyle c^{2}=a^{2}+a^{2}$ I get $\displaystyle \frac{c}{\sqrt{2}}=a$

Thanks.