{"id":5682,"date":"2021-03-05T15:26:52","date_gmt":"2021-03-05T09:56:52","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=5682"},"modified":"2021-09-15T11:39:28","modified_gmt":"2021-09-15T06:09:28","slug":"ap-board-9th-class-maths-solutions-chapter-8-intext-questions","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-9th-class-maths-solutions-chapter-8-intext-questions\/","title":{"rendered":"AP Board 9th Class Maths Solutions Chapter 8 Quadrilaterals InText Questions"},"content":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions<\/a> Chapter 8 Quadrilaterals InText Questions and Answers.<\/p>\n

AP State Syllabus 9th Class Maths Solutions 8th Lesson Quadrilaterals InText Questions<\/h2>\n

\"AP<\/p>\n

Try This<\/strong><\/p>\n

Question
\nExtend AB to E. Find \u2220CBE. What do you notice? What kind of angles are \u2220ABC and \u2220CBE?
\nSolution:
\nGiven that \u25a1ABCD is a parallelogram and\u2220A = 40\u00b0
\n\u2234 \u2220ABC = 180\u00b0-40\u00b0 = 140\u00b0
\n\u2220CBE = 40\u00b0 ( \u2235 \u2220A and, \u2220CBE are corresponding angles) And \u2220CBE and \u2220ABC are linear pair of angles.<\/p>\n

Do This<\/strong><\/p>\n

Question
\nCut out a parallelogram from a sheet of paper again and cut along one of its diagonal. What kind of shapes you obtain ? What can you say about these triangles 7 [Page No. 179]
\nSolution:
\nWe get two triangles.
\n\"AP
\nThe two triangles are congruent to each other.<\/p>\n

Think, Discuss and Write<\/strong><\/p>\n

Question 1.
\nShow that the diagonals of a square are equal and right bisectors of each other. (Page No. 185)
\nSolution:
\n\"AP
\nLet \u25a1ABCD be a square.
\nThus AB = BC = CD = DA
\nIn \u0394ABC and \u0394BAD
\nAB = AB (common base)
\n\u2220B =\u2220A (each 90\u00b0)
\nBC = AD (equal sides)
\n\u2234 \u0394ABC = \u0394BAD (SAS congruence)
\n\u21d2 AC = BD (CPCT)
\nAlso in \u0394AOB and \u0394COD
\n\u2220OAB = \u2220OCD [\u2235 alt. int. angles]
\n\u2220OBA = \u2220ODC [\u2235 alt. int. angles]
\nAB = DC (sides of a square)
\n\u2234 \u0394AOB = \u0394COD (ASA congruence)
\nThus AO = OC (CPCT) \u21d2 O is midpoint of AC
\nAlso BO = OD (CPCT) \u21d2 O is midpoint of BD
\n\u2234 O is midpoint of both AC and BD.
\n\u2234 Diagonals bisect each other.
\nIn \u0394AOB and \u0394COB
\nAB = BC (given)
\nOB = OB (common)
\nAO = OC (proved)
\n\u2234 \u0394AOB \u2245 \u0394COB (SSS congruence)
\n\u2220AOB = \u2220COB (CPCT)
\nBut \u2220AOB + \u2220COB = 180\u00b0 (\u2235 linear pair of angles)
\n\u2234 \u2220AOB = \u2220COB = 180\u00b0\/2 = 90\u00b0
\nAlso \u2220AOB = \u2220COD (\u2235 vertically opposite angles)
\n\u2220BOC = \u2220AOD (\u2235 vertically opposite angles)
\n\u2234 AC \u22a5 BD
\n(i.e.,) In a square diagonals bisect at right angles.<\/p>\n

Question 2.
\nShow that the diagonals of a rhombus divide it into four congruent triangles. (Page No. 185)
\nSolution:
\n\"AP
\n\u25a1ABCD is a rhombus
\nLet AC and BD meet at ‘O’
\nIn \u0394AOB and \u0394COD
\n\u2220OAB = \u2220ODC (alt.int.angles)
\nAB = CD (def. of rhombus)
\n\u2220OBA = \u2220ODC (alt. mt, angles)
\n\u2234 \u0394AOB \u2245\u0394COD …………(1)
\n(ASA congruence)
\nThus AO = OC (CPCT
\nAlso \u0394AOD \u2245 \u0394COD …………..(2)
\n[ \u2235AO = OC; AD = CD; OD = OD SSS congruence]
\nSimilarly we can prove
\n\u0394AOD \u2245 \u0394COB …………..(3)
\nFrom (1), (2) and (3) we have
\n\u0394AOB = \u0394BOC = \u0394COD = \u0394AOD
\n\u2234 Diagonals of a rhombus divide it into four congruent triangles.<\/p>\n

Try This<\/strong><\/p>\n

Question
\nDraw a triangle ABC and mark the mid points E and F of
\ntwo sides of triangle. \\(\\overline{\\mathbf{A B}}\\) and \\(\\overline{\\mathbf{A C}}\\) respectively. Join the point E and F as shown in the figure. Measure EF and the third side BC of triangle. Also measure \u2220AEF and \u2220ABC.
\nWe find \u2220AEF = \u2220ABC and \\(\\overline{\\mathrm{EF}}=\\frac{1}{2} \\overline{\\mathrm{BC}}\\)<\/p>\n

As these are corresponding angles made by the transversal AB with lines EF and BC, we say EF\/\/BC.
\nRepeat this activity with some more triangles. (Page No. 188)
\n\"AP
\nSolution:
\n\"AP
\nP, Q are mid points of XY and XZ
\nPQ \/\/ YZ
\nPQ = \\(\\frac{1}{2}\\)YZ<\/p>\n

\"AP
\nX, Y are mid points of PQ and PR
\nXY \/\/ QR
\nXY = \\(\\frac{1}{2}\\)QR<\/p>\n

\"AP
\nA, B are midpoints of DE and DF
\nAB \/\/ EF
\nAB = \\(\\frac{1}{2}\\)EF
\n( \u2235 In all cases the pairs of respective corresponding angles are equal.)<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions Chapter 8 Quadrilaterals InText Questions and Answers. AP State Syllabus 9th Class Maths Solutions 8th Lesson Quadrilaterals InText Questions Try This Question Extend AB to E. Find \u2220CBE. What do you notice? What kind of angles are \u2220ABC and \u2220CBE? Solution: Given that \u25a1ABCD is a parallelogram …<\/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\/5682"}],"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=5682"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/5682\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=5682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=5682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=5682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}