Answers

2015-05-26T10:22:21+05:30
Theorem: In right angle triangle, the square of hypotenuse is equal to the sum of the squares of the other two sides

Given: ΔABC is a right angled triangle, right angled at B

RTP: AC² = AB² + BC²

Construction: Draw BD perpendicular to AC

Proof: ΔABD is similar to ABC
          ⇒ AD / AB = AB / AC
               AD×AC = AB²  ------------------------- (1)
 
          Also, ΔBDC is similar to ΔABC
          ⇒ CD / BC = BC / AC
              CD × AC = BC²   ---------------------- (2)

          By adding (1) and (2),
         AD×AC + CD×AC = AB² + BC²
         AC ( AD+CD) = AB² + BC²
         AC (AC) = AB² + BC²
Therefore,
          AC² = AB² + BC²
         Hence, it is proved

         


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