step 1 is given. step 2, angles B and C are vertical, meaning they are 'pointing' at each other as one could say. step 3, angles C and E are both on the inside of lines R and G, which proves that they are same-side interior angles. step 4, just like B and C, E and H are vertical angles ('pointing' at each other). step 5 uses substitution because its showing that B is congruent to C, C is congruent to E, E is congruent to H, so by compressing that statement up it would lead us to proving that B is indeed congruent to H.
