Stephen is making a map of his neighborhood. He knows the following information:

His home, the bus stop, and the grocery store are all on the same street.
His home, the park, and his friend's house are on the same street.

http://prntscr.com/96mmsf

Stephen wants to use the Corresponding Angles Theorem to determine if the street between the park and bus stop is parallel to the street between his friend's house and the grocery store. He knows the angle between the bus stop, the park, and his home. Which other angle does he need to know?

Question

Stephen is making a map of his neighborhood. He knows the following information:

His home, the bus stop, and the grocery store are all on the same street.
His home, the park, and his friend's house are on the same street.

http://prntscr.com/96mmsf

Stephen wants to use the Corresponding Angles Theorem to determine if the street between the park and bus stop is parallel to the street between his friend's house and the grocery store. He knows the angle between the bus stop, the park, and his home. Which other angle does he need to know?

leahhhmorgannn · Answer

Bus stop, his home, and park
 Friend's house, grocery store, and bus stop
 Grocery store, his friend's house, and his home
 Park, bus stop, and his friend's house

leahhhmorgannn · Answer

@TheSmartOne

thesmartone · Answer

I gtg for a few minutes, maybe @jim_thompson5910 can help :)

jim_thompson5910 · Answer

first thing I would do is assign single letters to each point. I picked the first letter of each word

eg: Home ----> point H

see attached

jim_thompson5910 · Answer

`He knows the angle between the bus stop, the park, and his home`

so he knows angle BPH

leahhhmorgannn · Answer

and he's looking for corresponding angles, right?

jim_thompson5910 · Answer

yes

leahhhmorgannn · Answer

so a corresponding angle to BPH would be... GFP? 
sorry if that's wrong, can't concentrate very well right now.

jim_thompson5910 · Answer

GFP is the same as what angle (hint: they overlap) ?

leahhhmorgannn · Answer

it's honestly hard for me to find when it's drawn on that kind of triangle...

jim_thompson5910 · Answer

hopefully you see that it's GFH ?

jim_thompson5910 · Answer

angle GFP = angle GFH are overlapping angles

leahhhmorgannn · Answer

oh yeah, I see it now.

leahhhmorgannn · Answer

so what do we do to get back to BPH? I'm still a bit confused, sorry

jim_thompson5910 · Answer

angle BPH & angle GFH are corresponding angles

he knows angle BPH
if he knew that angle BPH = angle GFH, then he could use the corresponding angles theorem to prove the lines PB and FG are parallel

leahhhmorgannn · Answer

so angle GFH is all they were looking for as an answer, right? just the corresponding angle?

leahhhmorgannn · Answer

and GFH is grocery store, friend's house, and home..

jim_thompson5910 · Answer

`He knows the angle between the bus stop, the park, and his home.`
translation: he knows angle BPH

`Which other angle does he need to know?`
he needs to know GFH which is the angle between the `grocery store, friend's house, and home`

yes correct

leahhhmorgannn · Answer

Okay, thanks for helping me sort that out.

jim_thompson5910 · Answer

np