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Last updated at Aug. 13, 2018 by Teachoo

Transcript

Theorem 6.9: In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite to the first side is a right angle. Given: A triangle ABC in which γπ΄πΆγ^2=γπ΄π΅γ^2+γπ΅πΆγ^2 To Prove: β B=90Β° Construction: Draw Ξ PQR right angled at Q, such that PQ = AB and QR = BC. Proof: In βPQR β Q=90Β° By Pythagoras theorem, γππ γ^2=γππγ^2+γππ γ^2 Since PQ = AB and QR = BC γππ γ^2=γπ΄π΅γ^2+γπ΅πΆγ^2 Also, given that γπ΄πΆγ^2=γπ΄π΅γ^2+γπ΅πΆγ^2 From (1) & (2) γππ γ^2=γπ΄πΆγ^2 PR = AC In Ξ ABC & Ξ PQR AC = PR AB = PQ BC = QR β΄ Ξ ABC β Ξ PQR β β B = β Q Since β Q = 90Β° β΄ β B = 90Β° Hence Proved.

Theorems

Theorem 6.1 - Basic Proportionality Theorem (BPT)
Important

Theorem 6.2 - Converse of Basic Proportionality Theorem

Theorem 6.3

AA Similarity Criteria

Theorem 6.4

Theorem 6.5

Theorem 6.6 Not in Syllabus - CBSE Exams 2021

Theorem 6.7 Important Not in Syllabus - CBSE Exams 2021

Theorem 6.8

Theorem 6.9 You are here

Chapter 6 Class 10 Triangles

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.