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Similar Triangle Pythagoras Theorem
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Similar Triangle: Pythagoras Theorem
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
     PR2 = PQ2 + QR2
 
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Example : if PQR is an equilateral triangle of side 2a , prove that altitude
PS = a3.
Solution: in PQS and PRS ,
PQ = PR (Given)
PS = PS
And PSQ = PSR (each 90)
  PQS PRS (RHS)
Hence, QS = SR
or QS = SR = 1 / 2 * 2a = a
Now From PQS 
  PQ2 = QS2 +PS2 (Pythagoras Theorem)
or, (2a)2 = a2 + PS2
or, PS2 = 4a2 - a2= 3a2
or, PS = 3 a
 
 
   
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