Indeed, in your schoolbook, an “isosceles trapezoid” isn’t one with two equal sides, or with two equal angles; it is one that can be flipped without changing it. The post-Euclidean notion of symmetry has crept in, and it’s there because our minds are built to find it. More and more geometry classes are placing the idea of symmetry at the center, and building structures of proof starting from there. It’s not Euclid, but it’s where geometry is now.
