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 You are here

Theorem 6.8 Important Deleted for CBSE Board 2024 Exams

Theorem 6.9 Deleted for CBSE Board 2024 Exams

Last updated at April 16, 2024 by Teachoo

Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then right triangle on both sides of the perpendicular are similar to the whole triangle and to each other Given: ∆ABC right angled at B & perpendicular from B intersecting AC at D. (i.e. BD ⊥ AC) To Prove: ∆ADB ~ ∆ABC ∆BDC ~ ∆ABC & ∆ADB ~ ∆BDC Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then right triangle on both sides of the perpendicular are similar to the whole triangle and to each other Given: ∆ABC right angled at B & perpendicular from B intersecting AC at D. (i.e. BD ⊥ AC) To Prove: ∆ADB ~ ∆ABC ∆BDC ~ ∆ABC & ∆ADB ~ ∆BDC Proof: In ∆ADB & ∆ABC ∠ A = ∠ A ∠ ADB = ∠ ABC ∆ADB ~ ∆ABC Similarly, In ∆BDC & ∆ABC ∠ C = ∠ C ∠ BDC = ∠ ABC ∆BDC ~ ∆ABC From (1) and (2) ∆ADB ~ ∆ABC & ∆BDC ~ ∆ABC If one triangle is similar to another triangle, and second triangle is similar to the third triangle, then first and third triangle are similar ∴ ∆ADB ~ ∆BDC Hence Proved Rough This is same as a = b, b = c then a = c