{"id":4100,"date":"2021-02-26T12:23:33","date_gmt":"2021-02-26T06:53:33","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=4100"},"modified":"2021-09-15T11:40:39","modified_gmt":"2021-09-15T06:10:39","slug":"ap-board-9th-class-maths-solutions-chapter-3-ex-3-1","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-9th-class-maths-solutions-chapter-3-ex-3-1\/","title":{"rendered":"AP Board 9th Class Maths Solutions Chapter 3 The Elements of Geometry Ex 3.1"},"content":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions<\/a> Chapter 3 The Elements of Geometry Ex 3.1 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 9th Class Maths Solutions 3rd Lesson The Elements of Geometry Exercise 3.1<\/h2>\n

Question 1.
\nAnswer the following:
\ni) How many dimensions a solid has ?
\nSolution:
\nA solid has three dimensions namely length, breadth and height or depth.<\/p>\n

ii) How many books are there in Euclid’s Elements ?
\nSolution:
\nThere are 13 volumes in Euclid’s elements.<\/p>\n

\"AP<\/p>\n

iii) Write the number of faces of a cube and cuboid.
\nSolution:
\nCube : 6 faces
\nCuboid : 6 faces<\/p>\n

iv) What is the sum of interior angles of a triangle ?
\nSolution:
\nThe sum of interior angles of a triangle is 180\u00b0.<\/p>\n

v) Write three undefined terms of geometry.
\nSolution:
\nPoint, line and plane are three undefined terms in geometry.<\/p>\n

Question 2.
\nState whether the following statements are true or false. Also give reasons for your answers.
\na) Only one line can pass through a given point
\nb) All right angles are equal
\nc) Circles with same radii are equal
\nd) A finite line can be extended on its both sides endlessly to get a straight line
\n\"AP
\ne) From figure AB > AC
\nSolution:
\na) Only one line can pass through a given point – False.
\nReason : (Since, infinitely many lines can pass through a given point)
\nb) All right angles are equal – True.
\nc) Circles with same radii are equal – True.
\nd) A finite line can be extended on its both sides endlessly to get a straight line – True.
\ne) From figure AB > AC – True.<\/p>\n

\"AP<\/p>\n

Question 3.
\nIn the figure given below, show that the length AH > AB + BC + CD.
\n\"AP
\nSolution:
\nGiven a line \\(\\stackrel{\\leftrightarrow}{\\mathrm{AH}}\\)
\nTo prove AH > AB + BC + CD
\nFrom the figure AB + BC + CD = AD
\nAD is a part of whole AH.
\nFrom Euclid’s axiom whole is greater than part.
\n\u2234 AH > AD
\n\u21d2 AH > AB + BC + CD<\/p>\n

Question 4.
\nIf a point Q lies between two points P and R such PQ = QR, prove that PQ = \\(\\frac{1}{2}\\)PR.
\n\"AP
\nLet PR be a given line.
\nGiven that PQ = QR
\ni. e., Q is a point on PR.
\n\u21d2 PQ + QR = PR
\n\u21d2 PQ + PQ = PR [\u2235 PQ = QR]
\n\u21d2 2PQ = PR
\n\u21d2 PQ = \\(\\frac{1}{2}\\) PR
\nHence proved.<\/p>\n

\"AP<\/p>\n

Question 5.
\nDraw an equilateral triangle whose sides are 5.2 cm
\nSoluton:
\nStep – 1 : Draw a line segment AB of length 5.2 cm. *
\nStep – 2 : Draw an arc of radius 5.2 cm with centre A.
\nStep – 3 : Draw an arc of radius 5.2 cm with centre B.
\nStep – 4 : Two arcs intersect at C; join C to A and B.
\n\"AP
\n\u0394 ABC is the required triangle.<\/p>\n

Question 6.
\nWhat is a conjecture? Give an example for it.
\nSolution:
\nMathematical statements which are neither proved nor disproved are called conjectures. Mathematical discoveries often start out as conjectures. This may be an educated guess based on observations.
\nEg : Every even number greater than 4 can be written as sum of two primes. This example is called Gold Bach Conjecture<\/p>\n

Question 7.
\nMark two points P and Q. Draw a line through P and Q. Now how many lines are parallel to PQ, can you draw ?
\nSolution:
\n\"AP
\nInfinitely many lines parallel to PQ can be drawn.<\/p>\n

Question 8.
\nIn the figure given below, a line n falls on lines \/ and m such that the sum of the interior angles 1 and 2 is less than 180\u00b0, then what can you say about lines l and m ?
\n\"AP
\nSolution:
\nGiven : l, m and n are lines, n is a transversal.
\n\u22201 < 90\u00b0
\n\u22202 < 90\u00b0
\nIf the lines l and m are produced on the side where angles 1 and 2 are formed, they intersect at one point.<\/p>\n

\"AP<\/p>\n

Question 9.
\nIn the figure given below, if \u22201 = \u22203, \u22202 = \u22204 and \u22203 = \u22204 write the rela-tion between \u22201 and \u22202 using Euclid’s postulate.
\n\"AP
\nSolution :
\nGiven : \u22201 = \u22203
\n\u22203 = \u22204
\n\u22202 = \u22204
\n\u2234\u22201 = \u22202<\/p>\n

\u2235Both \u22201 and \u22202 are equal to \u22204. (By Euclid’s axiom things which are equal to same things are equal to one another).<\/p>\n

\"AP<\/p>\n

Question 10.
\nIn the figure given below, we have BX = \\(\\frac{1}{2}\\) AB, BY= \\(\\frac{1}{2}\\) BC and AB = BC. Show that BX = BY.
\n\"AP
\nSolution:
\nGiven : BX = \\(\\frac{1}{2}\\) AB
\nBY = \\(\\frac{1}{2}\\)BC
\nAB = BC
\nTo prove : BX = BY
\nProof: Given AB = BC [ \u2235 By Euclid’s axiom things which are halves of the same things are equal to one another]
\n\\(\\frac{1}{2}\\) AB = \\(\\frac{1}{2}\\) BC
\nBX = BY
\nHence proved.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions Chapter 3 The Elements of Geometry Ex 3.1 Textbook Questions and Answers. AP State Syllabus 9th Class Maths Solutions 3rd Lesson The Elements of Geometry Exercise 3.1 Question 1. Answer the following: i) How many dimensions a solid has ? Solution: A solid has three dimensions namely …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/4100"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=4100"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/4100\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=4100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=4100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=4100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}