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In Fig. 9.31, ABCD, DCFE and ABFE are p...

In Fig. 9.31, ABCD, DCFE and ABFE are parallelograms. Show that `a r (A D E) = a r(B C F)dot`

Text Solution

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In parallelogram, `ABCD`, `AD = BC`
In parallelogram, `DCFE`, `DE = CF`
In parallelogram, `ABFE`, `AE = AF`
Now, in `Delta ADE` and `Delta BCF`
`AD = BC`
`DE = CF`
`AE = AF`
So, from SSS criterion, `Delta ADE ~= Delta BCF`
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