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

Prove: △AMB ≅ △CMB

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Inscribed angle measures half its intercepted arc
∠ABM = ∠CBM
∠AMB = 90
arc AB = 180
Substitution
ASA (Angle-Side-Angle)
Reflexive
Inscribed angle measures half its intercepted arc
△AMB ≅ △CMB
Circle O with diameter AB, arc AM = arc DM
The angles in a linear pair are supplementary
Given
∠CMB = 90
∠ABM = (1/2) * arc AM and ∠CBM = (1/2) * arc DM
Substitution
MB = MB
∠AMB = (1/2) * arc AB
Definition