

Simple Geometry Puzzles You Can't Solve - nickb
http://thinkzone.wlonk.com/MathFun/Triangle.htm

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ingenium
I just solved the first one. Not that difficult. You draw two parallel lines
to line AB that intersect E and D. This creates a regular trapezoid. The
diagonals are congruent. I don't feel like writing out the rest of the steps,
but here is a link to the scanned image of it.

<http://www.hivgene.com/triangle1.png>

The answer is 10 btw.

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naish
I disagree. I got 20 (you can check it with a protractor if the figure is
drawn to scale). Triangle ADE is not isosceles. The diagonals within the
trapezoids are not parallel. The lower diagonal (BD) makes an angle of 60
degrees with AB; the upper diagonal (DE) is at 50 degrees from a line running
through D, parallel to AB.

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ingenium
Look at my work before you mod me down. The lines I drew were not drawn with a
ruler. If x is 10, then DE is 60 degrees from the line running through D (not
50), parallel to AB, just like the angle DBA.

If a protractor says one thing, and the math using known values says another,
I'm going to trust the math.

I see where according to the figure, triangle ADE must be isosceles, but I
don't trust that the figure is actually drawn to scale. All the measurements
of angles I got by calculations. Can you find a flaw in one of those?

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naish
Check again. The figure is to scale. I worked it out first and then checked
with a protractor. Your assumption that the diagonals within the trapezoids
are parallel is incorrect. As a result, angles that you have assigned to the
triangles in the upper trapezoid are also incorrect. The fact that triangle
ADE is not isosceles makes it impossible for x to be 10.

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rms
> Your assumption that the diagonals within the trapezoids are parallel is
> incorrect.

Do you mean his assumption that the diagonals within the trapezoids are
_congruent_ is incorrect? I'd be curious to see your diagram or proof to see
where you differ. Obviously, it makes a lot more sense that the diagram is
drawn to scale.

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naish
Here is my solution: <http://fernlabs.com/Problem1Solution.png>

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btw0
<http://mathcircle.berkeley.edu/BMC4/Handouts/geoprob.pdf>

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michelson01
answer is 42. I have a truly marvelous proof of this proposition which this
margin is too narrow to contain.

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nickb
Hahha... you managed to squeeze in two famous 'answers.'

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jamesbritt
Three, actually.

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lecktor
answer is 20. parallel line to line AB in D point gives us F point, after some
work we get EF=FD and angle FED=50, but angle AEB=30. So, here is the result
angle DEA = FEB - AEB = 20 : )

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daniel-cussen
Damn hard.

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aston
The first one isn't actually solvable; you get a system of equations with
infinite solutions. The second hint for it implies by looking at a drawing to
scale and putting in a few extra lines you'll get it, but it sounds more like
you're eyeballing angles. You might as well just pull out the protractor.

