For circles, it is well known that all inscribed angles are congruent. With the definition of inscribed angles maintained to ellipses, are all inscribed angles of an ellipse congruent?
HINT: Let us imagine an ellipse, where major axis is very large with comparison to minor axis. Consider two triangles: the first with two equal and the second with two very different edges (the third is major axis).
If you apply special cases of generally established results it is ok. You cannot always generalize results of particular situations that easily, without including all features correctly together.
In a circle there is a single center. In an ellipse there are two centers, the foci. So then how can you generalize?