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 2025 Exams

Theorem 6.7 Important Deleted for CBSE Board 2025 Exams

Theorem 6.8 Important Deleted for CBSE Board 2025 Exams You are here

Theorem 6.9 Deleted for CBSE Board 2025 Exams

Last updated at April 16, 2024 by Teachoo

Theorem 6.8 (Pythagoras Theorem) : If a right triangle, the square of the hypotenuse is equal to the sum of the squares of other two sides. Given: βABC right angle at B To Prove: γπ΄πΆγ^2= γπ΄π΅γ^2+γπ΅πΆγ^2 Construction: Draw BD β₯ AC Proof: Since BD β₯ AC Using Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of the a right triangle to the hypotenuse then triangle on both side of the perpendicular are similar to whole triangle and to each other. Ξ ADB βΌ Ξ ABC Since, sides of similar triangles are in the same ratio, β π΄π·/π΄π΅= π΄π΅/π΄πΆ βAD . AC= γπ΄π΅γ^2 Ξ BDC βΌ Ξ ABC Since, sides of similar triangles are in the same ratio β πΆπ·/π΅πΆ= π΅πΆ/π΄πΆ βCD . AC= γπ΅πΆγ^2 Adding (1) and (2) AD . AC + CD . AC = γπ΄π΅γ^2 + γπ΅πΆγ^2 AC (AD + CD) = γπ΄π΅γ^2 + γπ΅πΆγ^2 AC Γ AC = γπ΄π΅γ^2 + γπ΅πΆγ^2 γπ΄πΆγ^2 = γπ΄π΅γ^2 + γπ΅πΆγ^2 Hence Proved