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In △ABC,
(1) M is the mid point of AB and
MD∥BC
D is the mid point of AC
(2) As MD∥BC &
AC is transversal
∠MDC+∠BCD=180∘
∠MDC+90∘=180∘⇒∠MDC=90∘⇒MD⊥AC
(3) In △AMD and △CMD
AD=CD
∠ADM=∠CDM
DM=DM
△AMD≅△CMD
AM=CM⇒AM=½AB⇒CM=AM=½AB
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