2 established.

It is proved that BC=DC CG=CE angle BCG= Angle DCE, so two triangles are congruent triangles, so BG=DE. Let the intersection of DE with CG and BG be O and M respectively. Because two triangles are congruent, angle CED= angle CGB, and because angle EOC= angle GOM, two triangles are similar, so angle GMO= angle GCE=90 degrees, so BG = 90 degrees.

(2) Both of them are true, which is similar to the above proof method.