(Perfect Hacker: I hope you allow this)
Geometry it's beautiful!!!
Let's start a G-M
You know the rules, person who solves the problem, proposes the another one, but before proposing it, he must have the approval (if the answer is correct or not) of the person who proposed the previous geometry problem.
... and don't forget -no trig. allowed-. Use LaTeX.
Here's the first one
*)Translation: Euclid of Alexandria.
I don't have any fancy programs to d othe things you do, not yet atleast.
ΔBCD = 180 degrees,
<BDC = 180-45 = 135 degrees,
<BCD = 180 - 135 - x = 45 - x
ΔABC = 180 degrees,
<ABC = 180 - x - <BCA
ΔABD = 180 degrees,
<ABD = 180 - 45 - x = 135 - x
x = 30 degrees?
If that is true, <DBC must be 45 - 15 = 30, if that is true
ΔBCD = <BDC + <DBC + <BCD = 180 degrees
ΔBCD = 135 + 30 + 15 = 180 degrees
I could very well be wrong 'cause I'm just 14, and my notation sucks. The way I wrote it is understandable for me, but it may not be for others. It could also be that this is no proof at all, just some facts written down. If I happen to be right, someone else can go as I don't think I could make a good looking and well-thought problem.