```Date: Aug 20, 2012 7:14 PM
Author: Chuck
Subject: Re: Triangle similarity

> Books I have referenced mention various methods of> proving triangle similarity. One of these is that, if> two sides of a triangle are proportional to the> corresponding sides of another triangle, and the> included angles in each triange are equal, then the> triangles are similar. It seems to me that if two> sides of a triangle are proportional to corresponding> sides of a second triangle, and a not-included angle> is equal to the the corresponding not-included angle> of the other triangle, then the triangles are similar> also. But an examination of a few text books do not> mention this as a theorem. In fact, one text has this> as  a problem, and says the triangles cannot be> deemed similar in the  second case. Any opinions out> there?The reason it is not mentioned is that it is not true ingeneral.  Consider triangle ABC with <A = 30, AB = 10,BC = 6.  Now consider triangle DEF with <D = 30, DE = 5,and EF = 3.  You can draw triangle DEF with <F acute orwith <F obtuse (actually you can do the same thing with<C).  The situation is kind of like the ambiguity thatarises with SSA as a supposed method of congruence.  Theshape of the triangle is not uniquely determined.Chuck
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