Your turn: using the figure, a c = d a . what steps need to be taken to change this to a² = cd? example: multiply by 2; divide by a, etc

The first thing you should see in this case is that the triangles are proportional.
 We have then that:
 ((a) / (c)) = ((d) / (a))
 Step 1:
 Go a multiplying:
 ((a) / (c)) * (a) = (d)
 Step 2:
 Pass c multiplying:
 (a) * (a) = (d) * (c)
 Step 3:
 Same basis, exponents are added:
 a ^ (1 + 1) = (d) * (c)
 Step 4:
 a ^ 2 = c * d
 Finally
 ((a) / (c)) = ((d) / (a)) > a ^ 2 = c * d