How tension force is shown going through a body in this problem even though tension is a pulling force?

I was solving some problems about tension forces in my textbook and in solution of one problem I saw that one of the tension forces is drawn through the body,which confused me because text book was always drawing tension forces out of body(because it always pulls the body).

The Problem

Textbook Solution

The solutions follows like this:

I.$$T_{2} because its just a component of T3 obviously.

II.$$T_{1}=T_{5}$$ because purple tension forces cancel each other out.

III.$$T_{2}=T_{4}$$ because they are only horizontal and they cancel each other(green ones).

My Question I am actually confused at more than one point.These are point that I am confused at:

I. How did we know that T2 and T1 is component of T3 and do the two opposite T3 forces cancel each other out?

II. I dont get how we can say that there is T5 thats going through the body even though tension is a pulling force.

III. I am ok with this step because it is obvious.

I will appreciate any help and would be really happy if you can end my confusion.

• The solution that you were given is not very good. Apr 30 at 11:05

1. $$T_2$$ and $$T_1$$ are not components of $$T_3$$, they are equal to the horizontal and vertical components of $$T_3$$ respectively. I have already mentioned the reason why.