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In the figure, chord AB ~= chord CD ...

In the figure, chord AB `~= ` chord CD
Prove that ,
ar AC `~=` arc BD

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Chord `AB ~=` chord CD ….(Given )
`:.` Arc ACB `~=` arc CBD …(Arcs corresponding to congruent chords )
`:.` m (arc ACB ) = m (arc CBD ) ….(1)
But m ( arc ACB ) = m ( arc AC ) + m ( arc CB ) …..(2)
and m (arc CBD ) = m ( arc CB ) + m (arc BD ) ....(Arc addition postulate ) ....(3)
From (1 , (2) and (3) , we get
m (arc AC + m (arc CB ) = m (arc CB ) + m (arc BD )
`:. ` m (arc AC ) = m ( arc BD )
`:. ` arc `~=`` arc BD.
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