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pythagores Theovem

Posted by Sunithakumari Kg 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Mustafa Bhagat 5 years, 8 months ago

Given: A right-angled triangle ABC. To Prove- AC2 = AB2 + BC2 Pythagoras Theorem Proof Proof: First, we have to drop a perpendicular BD onto the side AC We know, △ADB ~ △ABC Therefore, ADAB=ABAC (Condition for similarity) Or, AB2 = AD × AC ……………………………..……..(1) Also, △BDC ~△ABC Therefore, CDBC=BCAC (Condition for similarity) Or, BC2= CD × AC ……………………………………..(2) Adding the equations (1) and (2) we get, AB2 + BC2 = AD × AC + CD × AC AB2 + BC2 = AC (AD + CD) Since, AD + CD = AC Therefore, AC2 = AB2 + BC2 Hence, the Pythagorean thoerem is proved

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