#### Chapters

Chapter 2 - Polynomials

Chapter 3 - Coordinate Geometry

Chapter 4 - Linear Equations in two Variables

Chapter 5 - Introduction to Euclid's Geometry

Chapter 6 - Lines and Angles

Chapter 7 - Triangles

Chapter 8 - Quadrilaterals

Chapter 9 - Areas of Parallelograms and Triangles

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Heron's Formula

Chapter 13 - Surface Area and Volumes

Chapter 14 - Statistics

Chapter 15 - Probability

## Chapter 5 - Introduction to Euclid's Geometry

#### Pages 85 - 86

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 produced indefinitely on both the sides.

(iv) If two circles are equal, then their radii are equal.

(v) In the following figure, if AB = PQ and PQ = XY, then AB = XY

Give a definition for parallel lines. Are there other terms that need to be defined first? What are they, and how might you define them?

Give a definition for perpendicular lines. Are there other terms that need to be defined first? What are they, and how might you define them?

Give a definition for line segment. Are there other terms that need to be defined first? What are they, and how might you define them?

Give a definition for radius of a circle. Are there other terms that need to be defined first? What are they, and how might you define them?

Give a definition for square. Are there other terms that need to be defined first? What are they, and how might you define them?

Consider two ‘postulates’ given below:-

(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.

(ii) There exist at least three points that are not on the same line.

Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.

If a point C lies between two points A and B such that AC = BC, then prove that Ac = 1/2AB. Explain by drawing the figure.

If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

In the following figure, if AC = BD, then prove that AB = CD.

Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)

#### Page 88

How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.