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ABC is a right triangle right angled at A. BCED, ACFG and ABMN aresquares on the sides BC, CA and AB respectively. Line segment `A X_|_D E`meets BCat Y. Show that:(i) `DeltaM B C~=DeltaA B D`(ii) `a r\ (B Y X D)\ =\ 2\

Text Solution

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`(i) In ΔMBC` and `ΔABD`, we have
`BC=BD` [Sides of the square BCED]
`MB=AB ` [Sides of the square ABMN]
and,`∠MBC=∠ABD`
Therefore, by SAS criterion of congruence, we have
`ΔMBC≅ΔABD`
...
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