ihuerta said: This discussion makes my eyes bleed and sort of makes me realiZe that people really don't know much math... like at all. Let's call the sides marked with one line as A, and those marked with two lines as B. Now, ASSUMING the lines in the diagram are straight, the two angles at the center of the figure have to be identical, as they are cuased by the interseccion of two straight lines. Lets say these angles have a value of ALPHA. Now, the Sin Rule says that A/sin(angle opposite A) = B/(sin opposite B) in a triangle. Therefore, since we know the anlge opposite both A's are the same (ALPHA), we therefore conclude that the angles opposibe B are also the same, let's call them BETA. |
ihuerta, before you go saying "people really don't know much math", you should really double-check your argument to be sure it holds up.
Your sine rule argument is a noble attempt, but it doesn't work. You know that (sin a)/A = (sin b)/B, but this does not prove that a = b even if A = B. For A = B and assuming that 0 < a < 180 degrees, and 0 < b < 180 degrees (since it's a triangle), for a given A, B, and a, there are exactly two values of b which satisfy (sin a)/A = (sin b)/B. One is an acute angle, the other is an obtuse angle (or it could be the degenerate case where they are both 90 degrees).
Think about it, if the sine rule argument worked, then side-side angle would always be a valid proof of congruency. It's been shown repeatedly here that side-side angle is not a valid proof of congruency.
I think this thread does show one very important thing about society: People will continue to argue back and forth even when the correct answer can be mathematically proven.
Looks like shams has drawn a very nice illustration of what I'm talking about. :)
