Last updated at May 29, 2018 by Teachoo

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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

Chapter 6 Class 10 Triangles

Example 5
Important

Example 8 Important

Example 10 Important

Example 14 Important

Theorem 6.1 - Basic Proportionality Theorem (BPT) Important

Theorem 6.7 Important

Ex 6.2, 4 Important

Ex 6.2, 5 Important

Ex 6.2, 6 Important

Ex 6.2, 9 Important

Ex 6.3, 11 Important

Ex 6.3, 12 Important

Ex 6.3, 13 Important

Ex 6.3, 14 Important

Ex 6.3, 15 Important

Ex 6.4, 1 Important

Ex 6.4, 3 Important

Ex 6.4, 5 Important

Ex 6.5, 2 Important

Ex 6.5, 3 Important You are here

Ex 6.5, 8 Important

Ex 6.5, 11 Important

Ex 6.5, 12 Important

Ex 6.5, 15 Important

Class 10

Important Questions for Exam - Class 10

- Chapter 1 Class 10 Real Numbers
- Chapter 2 Class 10 Polynomials
- Chapter 3 Class 10 Pair of Linear Equations in Two Variables
- Chapter 4 Class 10 Quadratic Equations
- Chapter 5 Class 10 Arithmetic Progressions
- Chapter 6 Class 10 Triangles
- Chapter 7 Class 10 Coordinate Geometry
- Chapter 8 Class 10 Introduction to Trignometry
- Chapter 9 Class 10 Some Applications of Trignometry
- Chapter 10 Class 10 Circles
- Chapter 11 Class 10 Constructions
- Chapter 12 Class 10 Areas related to Circles
- Chapter 13 Class 10 Surface Areas and Volumes
- Chapter 14 Class 10 Statistics
- Chapter 15 Class 10 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.