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In order to prove, 'In a right angled tr...

In order to prove, 'In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides
`(i)` Draw a near labelled figure.
`(ii)` Write 'Given' and 'To Prove' from the figure drawn by you.

Text Solution

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Proof`:` In `Delta PQR`,
`/_PQR = 90^(@)` …..(Given )
Seg QS `_|_` hypotenuse PR …(Construction )
`:. Delta PQR ~ Delta PSQ ~ Delta QSR ` ….(Similarity of rigth angled triangles ) …(1)
`Delta PQR ~ Delta PSQ` …[From (1) ]
`:. ( PQ)/( PR) = ( PS)/( PQ ) ` ..(Corresponding sides of similar triangles are in proportion)
`:. PQ^(2) = PS xx PR ` ...(2)
`Delta PQR ~ Delta QSR ` ....[From (1) ]
`:. (QR)/(PR) = (SR)/(QR)` ....(Corresponding sides of similar triangles are in proportion )
`:. QR^(2) = SR xx PR ` ...(3)
Adding (2) and (3), we get,
`PQ^(2) + QR^(2) = PS xxPR + SR xx PR `
`:. PQ^(2) + QR^(2) = PR ( PS+ SR) `
`:. PQ^(2) + QR^(2) = PR xx PR ` ...(P-S-R)
`:. PQ^(2) + QR^(2) = PR^(2) ` i.e., `PR^(2) = PQ^(2) + QR^(2)`
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