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Line-segment AB is parallel to another ...

Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see Fig. 7.15). Show that

(i) `DeltaA O B~=DeltaD O C`
(ii) O is also the mid-point of BC

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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