Question

Prove that angle congruence is not enough, by itself, to establish that two polygons are similar. Do this by describing or drawing two polygons that are not similar but whose corresponding angles are all congruent

Answer 1

The simplest example I can think of is a square and a rectangle: they both have 4 right angles, but they are not similar: the sides of a square are all the same length, the sides of a rectangle aren't.

So, there's no way you can start with a square and end with a rectangle by rotating/translating/dilating the shape. You'll need to squeeze the square along one direction only to get a square.

This means that the two shapes are not similar, even if they have the same angles.