Solution: make the vertical line AD of y axis and the vertical line AE of x axis.
Because angle ADB= angle AEC=90 degrees (vertical meaning)
So ad = 6, AE = 6.
DB=3, CE=3 (known)
In triangle ADB triangle AEC
AD=AE (authentication)
Angle ADB= angle AEC
BD=CE (certification)
So the triangle ADB is equal to the triangle AEC(S.A.S).
So AB=AC (the corresponding sides of congruent triangles are equal).
So triangle ABC is an isosceles triangle