I'm stuck on relations, more specific on how to determine if something is reflexive, symmetric, antisemmetric and transitive

I understand everyone but transitive, Yea, I've read and re-read the explanation (definition and i can come up with easy examples:

If (145)R(215) and (215)R(585) then (145)R(585)

What i don't get are how the examples and questions in the book can be transitive, if someone please could explain to me how in H*** these can be transitive, like point out the parts in bold and explain it to me like i'm a 3 year old would be great!

Here are the examples according to the book that are transitive:

--Example one---

A ={1,2,3}

R1 = {(1,1),(1,2),(1,3),(2,2),(2,3)(3,2)}

--Example two---

A={1,2,3,4}

R2 = {(1,1),(2,2),(3,3),(4,4),(1,2)}

Example three

A={1,2,3,4}

R2 = {(1,1),(2,2),(1,2),(2,1)}