Question 247498
I haven't tried geometry proofs in awhile.
so here goes.
we have two right triangles 
dbc and dba
we know that they are right triangles because db is perpendicualr to ac
we know that db=db
we also know that ba=bc since b is the midpoint of ac

we also know that angle dba is right angle as well as angle dbc

so we have  a right triangle with two legs that are equal therefore the hypotenuses are congruent since a^2+b^2=c^2 and we have the same legs (a and b) in both right triangles