Posted by Anonymous on Tuesday, January 20, 2009 at 7:19pm.
If you had two triangles, triangle RST and triangle UVW, and in triangle RST angle R= angle S= angle T and in triangle UVW angle U= angle V= angle W, is there enough information to prove that the triangles are congruent?
So each triangle is equiangular. But I don't know, is that enough to prove them congruent? Because aren't equiangular triangles also equilateral? What would the method be?

geometry  Reiny, Tuesday, January 20, 2009 at 9:04pm
No
To prove that two triangles are congruent you need at least one side of one triangle to be equal to that side in the other.
Having only angles equal would make them similar, that is, the corresponding angles are equal, and the corresponding sides are in the same ratio.
e.g.
suppose you have a any triangle, now create a new triangle by doubling each side of the original.
They certainly will not be congruent, but the corresponding angles of the the new and the old one would be equal.
an equilateral triangle has all its angles the same, namely 60 degrees.