What are the sides of a right angled isosceles triangle?

Let  abc be an isoscele right angle triangle, such
that:

ab = bc

angle b =
90

Since ab = bc , then angle a = angle
c

But angle a + angle c =
90

==> angle a = angle c =
45

We know that:

 cosa =
cos45

          = sqrt2/2 =
adjacent/hypotenuse

          =  sqrt2/2 = 
ab/ac

==> ab = bc =
sqrt2.....(sides)

==>
ac (hypotenuse) = 2