1.

`A B C D`is a parallelogram. `L`and `M`are points on `A B`and `D C`respectively and `A L=C Mdot`prove that `L M`and `B D`bisect each other.

Answer» AL=CM
AB-BL=CD-DM
-BL=-DM
BL=DM
NOW, AB||CD and traversal BD and LH
`/_3=/_4` and `/_1=/_2`
`In /_OBL and /_OMP`
`/_1=/_2`
`/_3=/_4`
BL=DM
`/_OBC cong /_ OMP(ASA)`
OB=OD and OL=OM
O is the mid point of BP and O is the midpoint of LM
BO and LM bisects each other at D.


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