The triangles don't have to be similar to make it a real pyramid. They only have to be similar of you want the truncation to be made parallel to the base. For

The triangles don't have to be similar to make it a real pyramid. They only have to be similar of you want the truncation to be made parallel to the base. For it to be a real pyramid, you only need the side edges lines to meet at the apex, which always happen when the top and bottom triangles are similar. Similar triangles are a sufficient, but not necessary condition.