Bractals
2006-08-22 20:42:41 |
Geometry - ASS
Is it generally accepted that if two triangles have corresponding angle-side-side and the angle is greater than or equal to a right angle, then the two triangles are congruent? |
brianjn
2006-08-22 21:00:18 |
Re: Geometry - ASS
Rephrasing-
My concept is: Two triangles are congruent if two sides and the included angle one are equal to the second (no matter what the size of the included angle - clearly cannot be 180 or 0) |
brianjn
2006-08-22 21:11:47 |
Re: Geometry - ASS
Pardon, I've just addressed the SAS case.
But yes, I would hold that in a situation where ASS of one triangle is the same as another, then you have congruence.
We also have ASA, SSS, but we cannot necessary have AAA since there is no indication of a side of common length. |
Bractals
2006-08-22 21:49:10 |
Re: Geometry - ASS
I think you need the requirement that the angle is greater than or equal to a right angle.
Aca : 30 degrees, sqrt(3), 1
Acab : 30 degrees, sqrt(3), 1, 1
Acab : 30 degrees, sqrt(3), 1, 2 |
Gamer
2006-08-22 22:03:55 |
Re: Geometry - ASS
You need something to distinguish between two possible triangles. One such way is with saying that an angle is obtuse. I think that's a lesser known theorom; I learned it when I took geometry. |
Bractals
2006-08-22 22:45:16 |
Re: Geometry - ASS
The reason I asked -
I saw a simple proof of the Steiner-Lehmus theorem that uses this property. |
brianjn
2006-08-23 01:47:24 |
Re: Geometry - ASS
This link says it all:
http://regentsprep.org/Regents/Math/congruen/Ltriangles.htm
I that the last one offered is likely to be the property about which you are concerned. |
