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In the ajoining figure , we haveangleABC...

In the ajoining figure , we have`angleABC=angleACBand angle3=angle4`. Show that BD=DC.

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Given , `angleABC=angleACB` ... (i)
and `angle4=angle3` ...(ii)
According to Eulid's axiom , if equals are subtracted from equals, then remainders are also equal. On subtracting Eq. (ii) From Eq.(i) we get
`angleABC-angle4=angleACB-angle3`
`rArr angle1=angle2`
Now , in `DeltaBDC , angle1=angle2`
`rArr` DC =BD [sides opposite to equales are equal]
`:.` BD=DC.
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