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In Figure, line segment A B is parallel ...

In Figure, line segment `A B` is parallel to another line segment `C D` . `O` is the mid-point of `A D` . Show that: ` aob~= D O C` `O` is also the mid-point of `B Cdot`

Text Solution

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Given:
`AB` is parallel to another line segment `CD`.
O is the midpoint of `AD`
In `triangleAOB and triangleDOC`
`angleAOB=angleCOD`
(Vertically opposite angle )
`angleBAO=angleCDO` ...(Given AB parallel to DC and AD meet both lines so alternate angles are equal)
`AO=OD` ....(O is the midpoint of AD )
`triangleAOBcongtriangleDOC`...`(ASA test)`
So, `BO=CO`Then, O is the midpoint of BC.
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