△AMB ≅ △CMB

arc AB = 180

∠CMB = 90

Substitution

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

∠AMB = 90

Reflexive

Given

Substitution

The angles in a linear pair are supplementary

Inscribed angle measures half its intercepted arc

Circle O with diameter AB, arc AM = arc DM

ASA (Angle-Side-Angle)

∠ABM = ∠CBM

Inscribed angle measures half its intercepted arc

MB = MB

∠AMB = (1/2) * arc AB

Definition