Form 2 Mathematics – PYTHAGORAS THEOREM msomimaktaba, November 13, 2018August 17, 2024 PYTHAGORAS THEOREMPYTHAGORAS THEOREM Pythagoras theorem is used to solve problems involving right angled triangles.Statement: In a right- angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.Shown belowRequired to prove: c2 = a2 + b2Construction : Joining L and N. Considering the trapezium PQLN:Area of the trapeziumbut area of trapezium = area Δ PKN + area Δ KQL + area Δ KLN(a+b) (a+b) = ab + ( c x c)(a+b) (a+b) = ab + c2 [a2 + 2ab + b2] = ab + c2a2 + ab + b2 = ab + c2a2 + b2 = c2a2 + b2 = c2 Pythagoras theorem Examples1.The side s of a triangle containing the right angle have length of 5cm and 12cm.Find the length of the hypotenuseSolutionC2= a2 +b2C2 = 52 + 122 C2 = 25+ 144C2 = 169C =C= 13cm∴The length of the hypotenuse = 13cm.In figure below if AC =17cm, BC = 8cm, and CD = 12cm find ADSolution: EXERCISECalculate the unknown side of the following triangleSOLUTION: 172 = 152 + b2b2 = 172 – 152b2 = 289 – 225b =b = 8cm∴ r2 = 82+ 82 r2 = 64 +64∴r =11.31cmGiven triangle ABC, where B = 900.Find the lengths of the sides which are not given A man travels 15km due north and then 8km due west. How far is he from his starting point?Solution:X2 = 152 +82X2 = 225 +64X =X = 17km ∴ He is 17km from his starting pointFind the area of the triangle and the length of the perpendicular from C to B.Solution: ALL NOTES FOR ALL SUBJECTS QUICK LINKS:AGRICULTURE O LEVEL PURE MATHEMATICS A LEVELBAM NOTES A LEVELBASIC MATH O LEVELBIOLOGY O/A LEVELBOOK KEEPING O LEVELCHEMISTRY O/A LEVELCIVICS O LEVELCOMPUTER(ICT) O/A LEVELECONOMICS A LEVELENGLISH O/A LEVELCOMMERCE O/A LEVELACCOUNTING A LEVELGENERAL STUDIES NOTESGEOGRAPGY O/A LEVELHISTORY O/A LEVELKISWAHILI O/A LEVELPHYSICS O/A LEVELMOCK EXAMINATION PAPERSNECTA PAST PAPERS Basic Mathematics Study Notes Form 2 Basic Mathematics Study Notes Msomi Maktaba All Notes FORM 2MATHEMATICSPost navigationPrevious postNext postRelated Posts Chemistry Study Notes Form 4 Chemistry – QUALITATIVE ANALYSIS November 12, 2018February 13, 2019ALL NOTES FOR ALL SUBJECTS QUICK LINKS: AGRICULTURE O LEVEL PURE MATHEMATICS A LEVEL BAM NOTES A LEVEL BASIC MATH O LEVEL BIOLOGY O/A LEVEL BOOK KEEPING O LEVEL CHEMISTRY O/A LEVEL CIVICS O LEVEL COMPUTER(ICT) O/A LEVEL ECONOMICS A LEVEL ENGLISH O/A LEVEL COMMERCE O/A LEVEL ACCOUNTING A LEVEL… Read More Economics Study Notes Form 6 Economics – STRUCTURE OF ECONOMY November 13, 2018April 26, 2020ALL NOTES FOR ALL SUBJECTS QUICK LINKS: AGRICULTURE O LEVEL PURE MATHEMATICS A LEVEL BAM NOTES A LEVEL BASIC MATH O LEVEL BIOLOGY O/A LEVEL BOOK KEEPING O LEVEL CHEMISTRY O/A LEVEL CIVICS O LEVEL COMPUTER(ICT) O/A LEVEL ECONOMICS A LEVEL ENGLISH O/A LEVEL COMMERCE O/A LEVEL ACCOUNTING A LEVEL… Read More Msomi Maktaba All Notes Tausi Portal: Ultimate Login and Registration Guide February 4, 2024Key Highlights The Tausi Tamisemi Portal is an online platform created by the Government of Tanzania, offering assistance to entrepreneurs and businesses in obtaining necessary permits and licenses from councils and municipalities. With the portal, Tanzania’s citizens can access government services at their own convenience, without visiting the government offices…. Read More Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment *Name * Email * Website Save my name, email, and website in this browser for the next time I comment. Δ
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