Geometry pythagorean theorem

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MATHPYTHAGOREAN THEOREMProof and ApplicationsPythagorean TheoremIn a right angles triangle, the square of the hypotenuse is equal to the sum of squares ofthe other two sides.Formula(Hypotenuse)2 = ( base )2 + ( height )2Consider a ∆le ABC right angled at B thenAC = hypotenuse, BC = base, AB = height⇒AC 2 = AB 2 + BC 2Proof:Construct BD ⊥ AC in ∆le ABCNow in ∆le ADB and ∆le ABC66BAD = 6 BAC(commonangle)ADB = 6 ABC = 90◦ (rightangle)According to AA similarity∆le ADB ∼ ∆le ABCADAB=⇒ AD · AC = AB 2⇒ABACIn the similar way ∆le BDC ∼ ∆le ABC ( accoding to AA similaxity )(1)⇒CDBC=⇒ CD · AC = BC 2BCAC(2)On adding equations (1) and (2)⇒ AD.AC + CD · AC = AB 2 + BC 2⇒ AC(AD + CD) = AB 2 + BC 2⇒ AC · AC = AB 2 + BC 2⇒ AC 2 = AB 2 + BC 2Hence Proved.Applications:1. It is used to find the thir … Purchase document to see full attachment

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