Given

∠ABM = ∠CBM

Substitution

△AMB ≅ △CMB

∠ABM = (1/2) * arc AM and ∠CBM = (1/2) * arc DM

ASA (Angle-Side-Angle)

Substitution

Inscribed angle measures half its intercepted arc

The angles in a linear pair are supplementary

∠CMB = 90

∠AMB = 90

Reflexive

Inscribed angle measures half its intercepted arc

arc AB = 180

Circle O with diameter AB, arc AM = arc DM

MB = MB

∠AMB = (1/2) * arc AB

Definition