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pythagores Theovem |
| Answer» Given: A right-angled triangle ABC.To Prove- AC2 = AB2 + BC2Pythagoras Theorem ProofProof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABCTherefore, CDBC=BCAC (Condition for similarity)Or, BC2= CD × AC ……………………………………..(2)Adding the equations (1) and (2) we get,AB2 + BC2 = AD × AC + CD × ACAB2 + BC2 = AC (AD + CD)Since, AD + CD = ACTherefore, AC2 = AB2 + BC2Hence, the Pythagorean thoerem is proved | |