Last updated at May 29, 2018 by Teachoo

Transcript

Example 14 O is any point inside a rectangle ABCD (see Fig. 6.52). Prove that OB2 + OD2 = OA2 + OC2. Given : Rectangle ABCD , and a point O inside rectangle . To prove :- OB2 + OD2 = OA2 + OC2 Proof :- Let us draw a line PQ, through O which is parallel to BC. Hence, PQ II BC ⇒ PQ II AD All angles of a rectangle are 90° , So, ∠ A = ∠ B = ∠ C = ∠ D = 90° Since, PQ II BC & AB is the transversal ∠ APO = ∠ B ∠ APO = 90° Similarly, we can prove ∠BPO = 90° , ∠ DQO = 90° & ∠CQO = 90° Using Pythagoras theorem. (Hypotenuse)2 = (Height)2 + (Base)2 Similarly, In right triangle ∆ 𝑂𝑄𝐶 , OC2 = OQ2 + CQ2 …(3) & In right triangle ∆ 𝑂𝐴𝑃 , OA2 = AP2 + OP2 …(4) Adding equation (1) and (2) OB2 + OD2 = BP2 + OP2 + OQ2 + DQ2 = (CQ)2 + (OP)2 + (OQ)2 + (AP)2 = CQ2 + OQ2 + OP2 + AP2 = OC2 + OA2 Thus, OB2 + OD2 = OC2 + OA2 Hence proved

Example 5
Important

Example 8 Important

Example 10 Important

Example 14 Important You are here

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

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.