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fbmagnumopus
Students
 
Posts: 39
Joined: Sat Aug 24, 2013 6:02 am
 

Q5 Pg 218 of the 3rd edition Geometry Strategy Guide

by fbmagnumopus Thu Sep 05, 2013 8:18 am

Hi
This is regarding Q5 Pg 218 of the 3rd edition Geometry Strategy Guide. In your solution, you’ve said that (on pg 229) triangles CDF and DFE ‘ have the same heights relative to bases CD and DE’. Can you please explain to me how we know that the height in question which I suppose is DF is a height indeed? What info exactly in the question/ figure tells us that FD is even perpendicular to CE for us to know that it’s a height? Is there a rule regarding the common vertex that leads to this outcome then?
Thanks any input on this question will be seriously appreciated given that its such a bouncer!
tommywallach
Manhattan Prep Staff
 
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Joined: Thu Mar 31, 2011 11:18 am
 

Re: Q5 Pg 218 of the 3rd edition Geometry Strategy Guide

by tommywallach Thu Sep 05, 2013 8:02 pm

Hey FB,

I agree with you that the explanation here isn't quite correct. We don't know if DF itself is the height, because the question has not definitively set it as meeting line CE perpendicularly.

Here's a better way to say it:

If you draw a line from any vertex of a triangle to the halfway point of the opposite side of the triangle, you MUST have divided that larger triangle in half, creating two triangles of equal area. Any other result simply wouldn't make any sense).

Hope that helps!

-t