Answer: The second proof table is the the proper proof table.
We always start out with what we are given, which in this case is r || s saying that r is parallel to s. Also, we always end up with what we want to prove which is angles b and h are supplementary. So this is the last line of the proof.
So far, this eliminates the first proof table because in this table, the last line says "angle c and angle h are supplementary" which is not what we want to end up with. We want the last line to say "angle b and angle h are supplementary".
We can also eliminate the third proof table because of the statement "angle d and angle h are supplementary". They are only supplementary if they are both right angles. Also, the reasoning of "alternate interior angles" is false as they are corresponding angles.
The only thing left is the second proof table which is correctly argued from start to finish.
1. r || s ........................ given
2. angle b = angle c ................ vertical angles
3. c and e are supplementary angles ....... same side interior
4. angle e = angle h ................. vertical angles
5. b and h are supplementary ...... substitution
Note: in line 5, we start with line 3's statement. Then we replace 'c' with 'b', at the same we replace 'e' with 'h'.
