Given: Circle O with diameter AB, arc AM = arc DM

Prove: △AMB ≅ △CMB

∠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