The "classic textbook proof" of equality of base angles of an isosceles triangles which I studied in my school days is as follows:
Let $\Delta ABC$ be a triangle with $AB = AC$ and let $D$ be the mid point of $BC$. Now the triangles $ADB$ and $ADC$ are congruent via $SSS$ criterion. Hence $\angle ABD = \angle ACD$ and this is the same as $\angle ABC = \angle ACB$.
I studied another proof some years ago in the Douglas R. Hofstadter's famous masterpiece Godel, Escher, Bach which was discovered by a computer program:
Consider the triangles $\Delta ABC, \Delta ACB$. These are congruent via $SSS$ criterion and hence $\angle ABC = \angle ACB$.
This one line proof is amazing, but at the same time looks confusing (some might think it is fishy but it is not) because the original triangle has been mirrored to exchange vertices $B, C$ and then considered congruent to original one.
My question is a pedagogic one:
Is this proof simpler to understand (compared to the standard version) for students of age 12-13 years? Should textbooks at least include this proof as well in some supplement or appendix?
Best Answer
That is a good idea. pay attention for postulates that you are accepted for doing proof. If students are familiar with postulates then it is very suitable to understand.