"c" is the hypotenuse of the largest triangle, and "a" is that triangle's shortest side. Thus the ratio is
... (longest side)/(shortest side)
Since all the triangles in the figure are similar, to complete the proportion, you need to recognize the triangle that "a" is the longest side of, then find the shortest side of that triangle.
"a" is the longest side (hypotenuse) of the smallest triangle. The shortest side of that triangle is "r". So, your proportion is ...
... c/a = a/r
The appropriate choice is the 2nd one, ...
... r
Answer:
The step 4 is not what he should have done. But the wrong is step 5, because if he added -2x both sides, it would give the following equation:

and not 
Note that in step 4 he should have added 2x and not -2x to both sides, but we still have the equality. The problem is that step 5 is totally wrong.
I don't know what answer is expected to this question, but I would mark step 5, because this is mathematically wrong.
Solving the equation

Using distribution

Add
both sides


Add 12 both sides

Divide both sides by 5



Hence they are similar
#2
- <A=<H
- And ratio of sides are same
Hence both triangles are similar by SAS property
#3

Since he deposited 160 then took out 160 it did not change