Chapter 5 Triangles Ex 5.2 eng
Chapter 5 Triangles Ex 5.2 Question 1. In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at 0. Join A to 0. Show that (i) OB = OC (ii) AO bisects ∠A Solution: (i) In ∆ ABC, we have AB = AC (Given) ⇒ ∠B = […]
Chapter 5 Triangles Ex 5.1 eng
Chapter 5 Triangles Ex 5.1 Question 1. In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see figure). Show that ∆ABC ≅ ∆ABD. What can you say about BC and BD? Solution: In ∆ABC and ∆ABD, we have AC = AD (Given) ∠ CAB = ∠ DAB (∵ AB bisects ∠A) and AB […]
Chapter 4 Lines and Angles Ex 4.3 eng
Chapter 4 Lines and Angles Ex 4.3 Question 1. In figure, sides QP and RQ of APQR are produced to points S and T, respectively. If ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ. Solution: Question 2. In figure, ∠X – 62°, ∠XYZ = 54°, if YO and ZO are the bisectors of ∠XYZ and […]
Chapter 4 Lines and Angles Ex 4.2 eng
Chapter 4 Lines and Angles Ex 4.2 Question 1. In figure, find the values of x and y and then show that AB || CD. Solution: ∵ x + 50° = 180° (Linear pair) ⇒ x = 130° ∴ y = 130° (Vertically opposite angle) Here, ∠x = ∠COD = 130° These are corresponding angles for […]
Chapter 4 Lines and Angles Ex 4.1 eng
Chapter 4 Lines and Angles Ex 4.1 Question 1. In figure, lines AB and CD intersect at 0. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE. Solution: Here, ∠AOC and ∠BOD are vertically opposite angles. ∴ ∠AOC = ∠BOD ⇒ ∠AOC = 40° [∵ ∠BOD = 40°(Given)] …(i) We […]
Chapter 3 Introduction to Euclid’s Geometry Ex 3.2 eng
Chapter 3 Introduction to Euclid’s Geometry Ex 3.2 Question 1. How would you rewrite Euclid’s fifth postulate so that it would be easier to understand? Solution: Two distinct intersecting lines cannot be parallel to the same line. Question 2. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain. Solution: Yes. According to Euclid’s fifth […]
Chapter 3 Introduction to Euclid’s Geometry Ex 3.1 eng
Chapter 3 Introduction to Euclid’s Geometry Ex 3.1 Question 1. Which of the following statements are true and which are false? Give reasons for your answers. (i) Only one line can pass through a single point. (ii) There are an infinite number of lines which pass through two distinct points. (iii) A terminated line can be […]
Chapter 2 Polynomials Ex 2.5 eng
Chapter 2 Polynomials Ex 2.5 Solution:(i) (x+ 4) (x + 10) Using identity (iv), i.e., (x+ a) (x+ b) = x2 + (a + b) x+ ab. We have, (x+4) (x + 10) = x2+(4 + 10) x + (4x 10) (∵ a = 4, b = 10) = x2 + 14x+40 (ii) (x+ 8) (x -10) Using identity […]
Chapter 2 Polynomials Ex 2.4 eng
Chapter 2 Polynomials Ex 2.4 Question 1.Determine which of the following polynomials has (x +1) a factor. (i) x3+x2+x +1 (ii) x4 + x3 + x2 + x + 1 (iii) x4 + 3×3 + 3×2 + x + 1 (iv) x3 – x2 – (2 +√2 )x + √2Solution: The zero of x + 1 is -1. (i) Let p (x) = x3 + […]
Chapter 2 Polynomials Ex 2.3 eng
Chapter 2 Polynomials Ex 2.3 Solution: Let p (x) = x3 + 3×2 + 3x + 1 (i) The zero of x+ 1 is – 1. (∵ x+ 1 = 0= x = -1) Question 2.Find the remainder when x3-ax2 +6x-ais divided by x – a.Solution: The zero of x – a is a. (∵ x – a […]