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 2023 Exams

Theorem 6.7 Important Deleted for CBSE Board 2023 Exams

Theorem 6.8 Important Deleted for CBSE Board 2023 Exams

Theorem 6.9 You are here

Chapter 6 Class 10 Triangles

Serial order wise

Last updated at Aug. 13, 2018 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.