Theorem 6.7 if perpendicular is drawn from the vertex of the right angle of right triangle to the hypotenuse.jpg

2 Theorem 6.7 ADB - BDC from (1) and  (2).jpg

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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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