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 Theorem 6.7 - Class 10th - If a perpendicular is drawn from the vertex of the right angle - Theorems

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  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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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, we can prove ∆BDC ~ ∆ABC From (1) and (2) ∆ADB ~ ∆ABC & , ∆ABC ~ ∆BDC ∴ ∆ADB ~ ∆BDC Hence Proved

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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