Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

Answer :

Here, C is the mid-point of line segment AB, such that AC = BC.

Let us assume that there are two mid-points C and C' of same line AB.

Then as already proved, AC = \(\frac{1}{2} \) AB and also, AC' = \(\frac{1}{2} \) AB

Therefore, we get, AC = AC' ,which is only possible when C and C’ Coincide.

Hence, it is proved that every line segment has one and only one mid-point.

- 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 figures, if AB=PQ and PQ=XY, then AB=XY.
- 2.Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they and how might you define them? (i) Parallel lines (ii) Perpendicular tines (iii) Line segment (iv) Radius of a circle (v) Square
- 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 atleast 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 = \(\frac{1}{2} \) AB, explain by drawing the figure.
- In 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.)

- NCERT solutions for class 9 maths chapter 1 Number Systems
- NCERT solutions for class 9 maths chapter 2 Polynomials
- NCERT solutions for class 9 maths chapter 3 Coordinate geometry
- NCERT solutions for class 9 maths chapter 4 Linear equations in two variables
- NCERT solutions for class 9 maths chapter 5 Introduction to Euclidean Geometry
- NCERT solutions for class 9 maths chapter 6 Lines and Angles
- NCERT solutions for class 9 maths chapter 7 Triangles
- NCERT solutions for class 9 maths chapter 8 Quadrilaterals
- NCERT solutions for class 9 maths chapter 9 Areas of parallelograms and triangles
- NCERT solutions for class 9 maths chapter 10 Circles
- NCERT solutions for class 9 maths chapter 11 Constructions
- NCERT solutions for class 9 maths chapter 12 Heron's Formula
- NCERT solutions for class 9 maths chapter 13 Surface areas and volumes
- NCERT solutions for class 9 maths chapter 14 Statistics
- NCERT solutions for class 9 maths chapter 15 Probability

- NCERT solutions for class 9 science chapter 1 Matter in our Surroundings
- NCERT solutions for class 9 science chapter 2 Is Matter Around Us Pure
- NCERT solutions for class 9 science chapter 3 Atoms and Molecules
- NCERT solutions for class 9 science chapter 4 Structure of the Atom
- NCERT solutions for class 9 science chapter 5 The Fundamental Unit of Life
- NCERT solutions for class 9 science chapter 6 Tissues and Fundamental unit of life
- NCERT solutions for class 9 science chapter 7 Diversity in Living Organisms
- NCERT solutions for class 9 science chapter 8 Motion
- NCERT solutions for class 9 science chapter 9 Force and Laws of Motion
- NCERT solutions for class 9 science chapter 10 Gravitation
- NCERT solutions for class 9 science chapter 11 Work and Energy
- NCERT solutions for class 9 science chapter 12 sound
- NCERT solutions for class 9 science chapter 13 Why do We Fall Ill
- NCERT solutions for class 9 science chapter 14 Natural Resources
- NCERT solutions for class 9 science chapter 15 Improvement in Food Resources