Similar Triangle Pythagoras Theorem

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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