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March 30th, 2012, 12:35 PM  #1 
Newbie Joined: Feb 2011 Posts: 8 Thanks: 0  Finding ratios of sides without any obvious similar triangle
I was given the following problem and cannot figure out how to relate AH to EH. I can't find a similar triangle despite having the brown vertical angle pair. I wasn't given any parallel lines either. 
March 30th, 2012, 07:20 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,534 Thanks: 1750 
Using vectors (effectively reducing the problem to solving simple simultaneous equations), I got AH/EH = 15/14, CD/BC = 23/19, and BH/HK = 35/23. 
March 30th, 2012, 07:53 PM  #3 
Newbie Joined: Feb 2011 Posts: 8 Thanks: 0  Re: Finding ratios of sides without any obvious similar tria
I don't understand how you would even set up equations. Are there similar triangles?

March 31st, 2012, 02:27 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,534 Thanks: 1750 
No. Just use the existing triangles. Assign each named point a position vector; it's convenient, but not essential, to make one of the points the origin. Since vector addition obeys the triangle rule, each triangle in the diagram corresponds to a simple vector equation. If you haven't used this concept before, also do web searches for topics such as "general vector form of the equation of a line" and "vector geometry", so that you can read up on the basic techniques (which are all you need).

April 1st, 2012, 07:39 AM  #5 
Newbie Joined: Feb 2011 Posts: 8 Thanks: 0  Re: Finding ratios of sides without any obvious similar tria
I'm familiar with vector addition but can't figure out how to set up the equations.

April 3rd, 2012, 02:39 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,534 Thanks: 1750 
If you've proceeded as suggested, please post what you can do (even if it doesn't get very far), using uppercase letters for vectors, and lowercase letters (or constants) for scalar multiples of them.


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