Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.5,3 In figure, ABD is a triangle right angled at A and AC β₯ BD. Show that AB2 = BC . BD Given: ABD is a triangle right angled at A . & AC β₯ π΅π· To prove: AB2 = BC . BD i.e. π΄π΅/π΅π· = π΅πΆ/π΄π΅ Proof: From theorem 6.7, If a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the Perpendicular are similar to the whole triangle and to each other So, Ξ BAD βΌ Ξ ACB If two triangles are similar , then the ratio of their corresponding sides are equal π΅π΄/π΅πΆ=π΅π·/π΅π΄ BA Γ BA = BD Γ BC BA2 = BD Γ BC i.e. AB2 = BD Γ BC Hence proved Ex 6.5,3 In figure, ABD is a triangle right angled at A and AC β₯BD. Show that (ii) AC2 = BC . DC We need to prove: AC2 = BC . DC i.e. π΄πΆ/π·πΆ = π΅πΆ/π΄πΆ From theorem 6.7, If a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the Perpendicular are similar to the whole triangle and to each other So, Ξ BCA βΌ Ξ ACD If two triangles are similar , then the ratio of their corresponding sides are equal π΅πΆ/π΄πΆ=πΆπ΄/πΆπ· BC Γ CD = AC Γ CA BC Γ CD = AC2 AC2 = BC Γ CD Hence proved Ex 6.5,3 In figure, ABD is a triangle right angled at A and AC β₯BD. Show that (iii) AD2 = BD . CD We need to prove: AD2 = BD . CD i.e. π΄π·/πΆπ· = π΅π·/π΄π· From theorem 6.7, If a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the Perpendicular are similar to the whole triangle and to each other So, Ξ DAB βΌ Ξ DCA If two triangles are similar , then the ratio of their corresponding sides are equal π·π΄/π·πΆ=π·π΅/π·π΄ DA Γ DA = DB Γ DC DA2 = DB Γ DC AD2 = BD Γ CD Hence proved

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.