Can you help me solve this geometry question?

Question

Triangle GAB is an isosceles triangle with vertex angle A and Triangle BCD is an isosceles triangle with vertex angle C. Is BGH congruent with BHD? Why. Explain your answer.

 

Picture:

 

   http://assets.openstudy.com/updates/attachments/52d747ffe4b0cb9c2bfca962-melmore-1389840534884-geo5.jpg

Answer 1

I found an image, but not sure if it is appropriate for this proof. I do not have access to the link above. But does the image have points A, B, C collinear as well as A, G, F collinear as well? Are there single hash marks on AG, and CB? Looks like I have also an equiangular triangle GFE. Let me know if this is the image. I can justify whether or not triangle BGH congruent with triangle BDH.