Thank you for the opportunity to help you with your question!

as di s the the midpoint of ac then ad = dc = ac/2

now <bda + bdc = 180 => <bda = <bdc = 90

now we just have to prove AB is equal to BC as all other parameters are equal that is AD=DC , BD is common in both and both triangles are right angles so

AB = √AD^2 +BD^2

BC = √BD^2 + CD^2

and we know that AD = CD so substituting CD in place AD we get AB = √CD^2 + BD^2

which is exactly equal to BC hence AB is also equal to BC

so we get

AB=BC

AD = CD

BD is common hence both triangles are identical.

Please let me know if you need any clarification. I'm always happy to answer your questions.