{"id":340,"date":"2020-09-07T10:11:24","date_gmt":"2020-09-07T04:41:24","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=340"},"modified":"2021-07-02T15:03:45","modified_gmt":"2021-07-02T09:33:45","slug":"kseeb-solutions-class-9-maths-chapter-2-ex-2-1","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-class-9-maths-chapter-2-ex-2-1\/","title":{"rendered":"KSEEB Solutions for Class 9 Maths Chapter 2 Introduction to Euclid Geometry Ex 2.1"},"content":{"rendered":"

KSEEB Solutions for Class 9 Maths Chapter 2 Introduction to Euclid Geometry Ex 2.1<\/strong> are part of KSEEB Solutions for Class 9 Maths<\/a>. Here we have given Karnataka Board Class 9 Maths Chapter 2 Introduction to Euclid Geometry Exercise 2.1.<\/p>\n

Karnataka Board Class 9 Maths Chapter 2 Introduction to Euclid Geometry Ex 2.1<\/h2>\n

Question 1.
\nWhich of the following statements are true and which are false? Give reasons for your answers.
\n(i) Only one line can pass through a single point.
\nAnswer:
\nFalse. A number of lines can pass through a single point.<\/p>\n

(ii) There is an infinite number of lines which pass through two distinct points.
\nAnswer:
\nFalse. Because there is a unique line that passes through two points.<\/p>\n

(iii) A terminated line can be produced indefinitely on both sides.
\nAnswer:
\nTrue. A terminated line can be produced indefinitely on both sides.<\/p>\n

(iv) If two circles\u2019 are equal, then their radii are equal.
\nAnswer:
\nTrue. Because the circumference of equal circles is equal their distance is the same from centre. Hence radii of two circles are equal.<\/p>\n

(v) In Fig 2.9, if AB = PQ and PQ = XY, then AB = XY.
\n\"KSEEB
\nAnswer:
\nTrue. Because E.g., If AB = 4 cm, PQ = 4 cm., then, AB = PQ = 4 cm.
\nPQ = XY = 4 cm.
\n\u2234 AB = PQ = XY
\n\u2234 AB = XY.<\/p>\n

Question 2.
\nGive 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?
\n(i) parallel lines
\n(ii) perpendicular lines
\n(iii) line segment
\n(iv) the radius of a circle
\n(v) square.
\nAnswer:
\n(i) Parallel Lines :
\n\"KSEEB
\nIf endpoints of two straight lines do not meet even if they are produced on both sides, they are called parallel lines.
\nBefore the definition concept of point, a straight line is necessary.
\nPoint: A point is that which has no part.
\nStraight-line: A straight line is a line which lies evenly with the points on itself.<\/p>\n

(ii) Perpendicular Lines:
\n\"KSEEB
\nIf Angle between \\(\\overrightarrow{\\mathrm{OA}}\\) and \\(\\overrightarrow{\\mathrm{OB}}\\) is 90\u00b0, then only lines are perpendicular mutually.
\nBefore the definition concept of Ray and Angle is necessary.
\nRay: Joining one endpoint and the non-end point is called Ray.
\n\"KSEEB
\nAngle:
\n\"KSEEB
\nRay \\(\\overrightarrow{\\mathrm{OA}}\\) and Ray \\(\\overrightarrow{\\mathrm{OB}}\\) revolve and forms an angle.<\/p>\n

(iii) Segment:
\n\"KSEEB
\nThe segment is formed when two endpoints are joined.
\nHere we must know the point and straight line.
\nPoint: It has only dimension, no length, breadth, and thickness.
\nA – Starting point
\nB – Endpoint
\nAB – Segment
\nStraight-line: When two endpoints of a segment is produced on both sides, we get a straight line.<\/p>\n

iv) The radius of a Circle :
\n\"KSEEB
\nA circle is a set of points that moves from a fixed point.
\nThat equal distance is the radius of the circle.
\n‘O’ – Fixed point
\nOA – radius of the circle.
\nNecessary terms – Point, Segment.<\/p>\n

v) Square :
\n\"KSEEB
\nA Square is a figure in which all sides and angles are equal.
\nAB = BC = CD = DA = 4 cms.
\n\u2220A = \u2220B = \u2220C = \u2220D = 90\u00b0.
\nNecessary terms – Quadrilateral, angle.
\nQuadrilateral In a plane, if 3 points in 4 points are non-collinear and meet in different points, such a figure is called a quadrilateral.
\nAngle: ‘O’ is common point between \\(\\overrightarrow{\\mathrm{OA}}\\) and \\(\\overrightarrow{\\mathrm{OB}}\\) Such figure is called an angle.<\/p>\n

Question 3.
\nConsider two \u2018postulates\u2019 given below :
\n(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.
\n(ii) There exist at least three points that are not on the same line.
\nDo these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid\u2019s postulates? Explain.
\nAnswer:
\nThere are many undefined terms for students.
\nThey are consistent because they deal with two different situations.
\n(i) When two points A and B are given, C is in between two.
\n(ii) When two points A and B are given take point C which passes through A and B.
\nThese postulates do not follow from Euclid’s postulates. But they follow Axiom 2.1<\/p>\n

Question 4.
\nIf a point C lies between two points A and B such that AC = BC, then prove that \\(A C=\\frac{1}{2} A B\\). Explain by drawing the figure.
\nAnswer:
\n\"KSEEB
\nData: C lies between A and B such that AC = BC.
\nTo Prove: AC = \\(\\frac{1}{2}\\)AB
\nProof: In this figure AC = BC.
\nAdding AC on both sides,
\nAC + AC = BC + AC (equals are added to equals)
\n2AC = BC + AC
\n2AC = AB (\u2235 BC + AC = AB)
\n\u2234 AC = \\(\\frac{1}{2}\\)AB.<\/p>\n

Question 5.
\nIn Question 4, point C is called a mid\u00acpoint of line segment AB. Prove that every line segment has one and only one mid-point.
\nAnswer:
\n\"KSEEB
\nLet C and D are two points lies on AB.
\nC is the mid-point of AB.
\nAC = BC
\nAdding AC on both sides,
\nAC + AC = BC + AC
\n2AC = AB \u2192 (i)
\nD is the mid-point of AB,
\nAD = DB
\nAdding AD on both sides,
\nAD + AD = DB + AD
\n2AD = AB \u2192 (ii)
\nFrom equations (i) and (ii),
\n2AC = 2 AD.
\n\u2234 AC = AD.
\nThen C and D are not different, they are the same.
\n\u2234 \u201cEvery segment has one and only one mid-point.”<\/p>\n

Question 6.
\nIn Fig. 2.10, if AC = BD, then prove that AB = CD.
\n\"KSEEB
\nAnswer:
\nData: In this figure AC = BD.
\nTo Prove : AB = CD
\nProof: AC = BD (Data) \u2192 (i)
\nBut, AC = AB + BC
\nand BD = BC + CD.
\nSubstituting the value of (i)
\nAC = BD
\n\"KSEEB
\n\u2234 AB = CD.<\/p>\n

Question 7.
\nWhy is Axiom 5, in the list of Euclid\u2019s axioms, considered a \u2018universal truth\u2019 ? (Note that the question is not about the fifth postulate).
\nAnswer:
\nEuclid\u2019s 5th Axiom of Euclid states that \u201cThe whole is greater than the part.”
\nThis is a universal truth. Because it is not applicable to Mathematics only. It is useful for all.
\nE.g. 1: ‘a’ is whole, \u2019b\u2019 and ‘c’ are its parts.
\na = b + c.
\nNow, a > b and a > c.
\nIt means a is greater than b.
\na is greater than c.
\nE.g 2: If the human body is full, fingers are its parts.
\n\u2234 \u201cHuman body is greater than-his fingers.\u201d<\/p>\n

We hope the KSEEB Solutions for Class 9 Maths Chapter 2 Introduction to Euclid Geometry Ex 2.1 help you. If you have any query regarding Karnataka Board Class 9 Maths Chapter 2 Introduction to Euclid Geometry Exercise 2.1, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"

KSEEB Solutions for Class 9 Maths Chapter 2 Introduction to Euclid Geometry Ex 2.1 are part of KSEEB Solutions for Class 9 Maths. Here we have given Karnataka Board Class 9 Maths Chapter 2 Introduction to Euclid Geometry Exercise 2.1. Karnataka Board Class 9 Maths Chapter 2 Introduction to Euclid Geometry Ex 2.1 Question 1. …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/340"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=340"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/340\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}