Check sibling questions

Ex 6.5, 3 - ABD is a triangle right angled at A & AC βŠ₯ BD - Ex 6.5

Ex 6.5, 3 - Chapter 6 Class 10 Triangles - Part 2

This video is only available for Teachoo black users

Ex 6.5, 3 - Chapter 6 Class 10 Triangles - Part 3
Ex 6.5, 3 - Chapter 6 Class 10 Triangles - Part 4

This video is only available for Teachoo black users

Ex 6.5, 3 - Chapter 6 Class 10 Triangles - Part 5
Ex 6.5, 3 - Chapter 6 Class 10 Triangles - Part 6

This video is only available for Teachoo black users


Transcript

Ex 6.5,3 In figure, ABD is a triangle right angled at A and AC βŠ₯ BD. Show that AB2 = BC . BD Given: ABD is a triangle right angled at A . & AC βŠ₯ 𝐡𝐷 To prove: AB2 = BC . BD i.e. 𝐴𝐡/𝐡𝐷 = 𝐡𝐢/𝐴𝐡 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 ∼ Ξ” ACB If two triangles are similar , then the ratio of their corresponding sides are equal 𝐡𝐴/𝐡𝐢=𝐡𝐷/𝐡𝐴 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 βŠ₯BD. Show that (ii) AC2 = BC . DC We need to prove: AC2 = BC . DC i.e. 𝐴𝐢/𝐷𝐢 = 𝐡𝐢/𝐴𝐢 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 ∼ Ξ” ACD If two triangles are similar , then the ratio of their corresponding sides are equal 𝐡𝐢/𝐴𝐢=𝐢𝐴/𝐢𝐷 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 βŠ₯BD. Show that (iii) AD2 = BD . CD We need to prove: AD2 = BD . CD i.e. 𝐴𝐷/𝐢𝐷 = 𝐡𝐷/𝐴𝐷 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 ∼ Ξ” DCA If two triangles are similar , then the ratio of their corresponding sides are equal 𝐷𝐴/𝐷𝐢=𝐷𝐡/𝐷𝐴 DA Γ— DA = DB Γ— DC DA2 = DB Γ— DC AD2 = BD Γ— CD Hence proved

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.