Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.5, 15 In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3BC. Prove that 9AD2 = 7 AB2 Given: Equilateral triangle ABC D is a point an BC Such that BD = 1/3 BC To prove: 9 AD2 = 7 AB2 Construction: Lets draw AE BC Proof: All sides of equilateral triangle is equal, AB = BC = AC Let AB = BC = AC = x Given BD = 1/3BC BD = /3 In AE = AE AB = AC = Hence by RHS congruency BE = EC So, BE = EC = 1/2BC BE = EC = /2 So, BE = /2 BD + DE = /2 /3+ = /2 DE = /2 /3 DE = (3 2 )/(2 3) DE = /6 Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 Similarly In right AD2 = AE2 + DE2 AD2 = 3 2/4+( /6 )^2 AD2 = 3 2/4+ 2/36 AD2 = ((3 2) 9 + 2)/36 AD2 = (27 2 + 2)/36 AD2 = (28 2)/36 AD2 = 7 2/9 9AD2 = 7x2 9 AD2 = 7 AB2 Hence proved

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

Ex 6.5, 8 Important

Ex 6.5, 11 Important

Ex 6.5, 12 Important

Ex 6.5, 15 Important You are here

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.