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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: 21,028 Thanks: 2259 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: 21,028 Thanks: 2259 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: 21,028 Thanks: 2259 If you've proceeded as suggested, please post what you can do (even if it doesn't get very far), using upper-case letters for vectors, and lower-case letters (or constants) for scalar multiples of them.

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### similar triangle ratio vector addition

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