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

ASA (Angle-Side-Angle)

∠ABM = ∠CBM

Given

Inscribed angle measures half its intercepted arc

Reflexive

∠AMB = 90

Substitution

Circle O with diameter AB, arc AM = arc DM

△AMB ≅ △CMB

Substitution

∠CMB = 90

The angles in a linear pair are supplementary

Inscribed angle measures half its intercepted arc

arc AB = 180

MB = MB

∠AMB = (1/2) * arc AB

Definition