Questions

Module 2 Week 2 Day 5 Challenge Part 1 Miniquestion
 Why does choice ii not work? Don't they share an angle at point B?
 Why does choice iii work? It feels like if two triangles are on the opposite of each other, they are congruent. That alone doesn't make a lot of sense to me.

@thebladedancer Thank you for asking!
The reason choice ii.) doesn't work is because if you look at transversal line \(\overline{AC}\) which crosses the two parallel lines \(\overline{CD}\) and \(\overline{AB},\) we find that \(\angle \textcolor{blue}{PAB}\) is congruent to \(\angle \textcolor{blue}{PCD}.\) We don't know if \(\angle \textcolor{blue}{PCD}\) is the same as the angle \(\angle \textcolor{orange}{BCP},\) so that's why choice ii.) is false.
The symbol "\(\angle\)" means "angle," rather than triangle, so in choice iii.) it says that \(\angle CPB\) and \(\angle DPA\) are equal; it's not implying that the two triangles \(\bigtriangleup PDA\) and \(\bigtriangleup PCB\) are congruent.
I hope this helps! Please let us know if you have more questions!

@debbie
Thank you, this was really helpful. 
@imadandelion You're welcome, and I'm glad it was useful!