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

Prove: Triangle AMB is congruent to Triangle CMB

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