"which statement is necessarily true if bd is an altitude to the hypotenuse of right δabc?

a.) δadb≅δbdc
b.) δadb~δbdc
c.) abbc=acbd
d.) ∠bac≅∠bdc"

This is the TRUE statement based on the given image. A.) ΔADB≅ΔBDC 

Triangle ADB:
Angle D = 90°
Angle B = 90°/2 = 45°
Angle A = 180° - 90° - 45° = 45°

So Triangle ADB is 90-45-45 triangle. 

Triangle BDC
Angle ? = 90° This is the angle that is adjacent to Angle D. It is also supplementary to Angle D.
Angle B = 90°/2 = 45°
Angle C = 180° - 90° - 45° = 45°

So, Triangle BDC is also a 90-45-45 triangle.