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March 30th, 2012, 01:35 PM   #1
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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.

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March 30th, 2012, 08:20 PM   #2
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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.
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March 30th, 2012, 08:53 PM   #3
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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?
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March 31st, 2012, 03:27 AM   #4
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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).
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April 1st, 2012, 08:39 AM   #5
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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.
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April 3rd, 2012, 03:39 AM   #6
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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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