I am about to 'prove' to you that ALL triangles are isosceles. That is, all triangles have two sides equal in length.

I do this by starting with any generic triangle, making a few constructions and then arguing carefully using my knowledge of congruent triangles. Now, you *know* that this conclusion is not true! So, you (correctly) conclude that I have made an error somewhere, or that I am deliberately misleading you ... but WHERE and HOW? That is the challenge.

This is a good way to learn some principles of geometry. Over to you.

As a bit of an aside, did you know that the term *isosceles* comes from the Greek for equal/same legs? Also fascinating is the term *scalene.* It also derives from the Greek, from a word *skalenos,* meaning uneven. I have read elsewhere that lame men were referred to using the same word (but have had difficulty finding the reference). So, equal legged triangles stood up straight and lame man triangles had unequal legs! It all makes sense, doesn't it?

I hope you enjoy your journey into the realm of geometry.