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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 Important

Theorem 6.5

Theorem 6.6 Important Deleted for CBSE Board 2024 Exams

Theorem 6.7 Important Deleted for CBSE Board 2024 Exams

Theorem 6.8 Important Deleted for CBSE Board 2024 Exams

Theorem 6.9 Deleted for CBSE Board 2024 Exams You are here

Last updated at May 29, 2023 by Teachoo

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.