Isosceles Triangle Theorem

Another result about triangles that is important and follows directly from SAS is the Isosceles Triangle Theorem.  An isosceles triangle is one that has two equal sides.  The Isosceles Triangle Theorem says that the angles opposite those sides will also be equal:

If  then :

Its converse is also true:  If two angles of a triangle are equal, then so are the sides opposite them.  That is, if , then .

Both of these results are almost obvious because an isosceles triangle is symmetric about a line splitting it in half:

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