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Theorem 6.7 - Class 10 - If a perpendicular is drawn from vertex of

Theorem 6.7 - Chapter 6 Class 10 Triangles - Part 2
Theorem 6.7 - Chapter 6 Class 10 Triangles - Part 3

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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 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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.