Questions
-
Module 2 Week 2 Day 5 Challenge Part 1 Mini-question
- 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.
-
@the-blade-dancer 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!
