{"id":4674,"date":"2021-03-01T16:52:24","date_gmt":"2021-03-01T11:22:24","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=4674"},"modified":"2021-09-15T11:40:36","modified_gmt":"2021-09-15T06:10:36","slug":"ap-board-9th-class-maths-solutions-chapter-8-ex-8-1","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-9th-class-maths-solutions-chapter-8-ex-8-1\/","title":{"rendered":"AP Board 9th Class Maths Solutions Chapter 8 Quadrilaterals Ex 8.1"},"content":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions<\/a> Chapter 8 Quadrilaterals Ex 8.1 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 9th Class Maths Solutions 8th Lesson Quadrilaterals Exercise 8.1<\/h2>\n

Question 1.
\nState whether the statements are true or false.
\ni) Every parallelogram is a trapezium.
\nii) All parallelograms are quadrilaterals.
\niii) All trapeziums are parallelograms.
\niv) A square is a rhombus.
\nv) Every rhombus is a square.
\nvi) All parallelograms are rectangles.
\nSolution:
\ni) True
\nii) True
\niii) False
\niv) True
\nv) False
\nvi) False<\/p>\n

\"AP<\/p>\n

Question 2.
\nComplete the following table by writing YES if the property holds for the particular quadrilateral and NO if property does not holds.
\n\"AP \"AP
\nSolution:
\n\"AP<\/p>\n

Question 3.
\nABCD is a trapezium in which AB || CD. If AD = BC, show that \u2220A = \u2220B and \u2220C = \u2220D.
\nSolution:
\nGiven that in \u25a1ABCD AB || CD; AD = BC
\nMark a point ‘E’ on AB such DC = AE.
\n\"AP
\nJoin E, C.
\nNow in AECD quadrilateral
\nAE \/\/ DC and AE = DC
\n\u2234 \u25a1AECD is a parallelogram.
\n\u2234 AD\/\/EC
\n\u2220DAE = \u2220CEB (corresponding angles) ……………..(1)
\nIn \u0394CEB; CE = CB (\u2235 CE = AD)
\n\u2234 \u2220CEB = \u2220CBE (angles opp. to equal sides) …………….. (2)
\nFrom (1) & (2)
\n\u2220DAE = \u2220CBE
\n\u21d2 \u2220A = \u2220B
\nAlso \u2220D = \u2220AEC (\u2235 Opp. angles of a parallelogram)
\n= \u2220ECB + \u2220CBE [ \u2235 \u2220AEC is ext. angle of \u0394BCE] |
\n= \u2220ECB + \u2220CEB [ \u2235\u2220CBE = \u2220CEB]
\n= \u2220ECB + \u2220ECD [\u2235 \u2220ECD = \u2220CEB alt. int. angles]
\n= \u2220BCD = \u2220C
\n\u2234 \u2220C = \u2220D<\/p>\n

\"AP<\/p>\n

Question 4.
\nThe four angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. Find the measure of each angle of the quadri-lateral.
\nSolution:
\nGiven that, the ratio of angles of a quad-rilateral = 1 : 2 : 3 : 4
\nSum of the terms of the ratio
\n= 1 +2 + 3 + 4= 10
\nSum of the four interior angles of a quadrilateral = 360\u00b0
\n\u2234 The measure of first angle
\n= \\(\\frac{1}{10}\\) \u00d7 360\u00b0 = 36\u00b0
\nThe measure of second angle
\n= \\(\\frac{2}{10}\\) \u00d7 360\u00b0 = 72\u00b0
\nThe measure of third angle
\n= \\(\\frac{3}{10}\\) \u00d7 360\u00b0 = 108\u00b0
\nThe measure of fourth angle
\n= \\(\\frac{4}{10}\\) \u00d7 360\u00b0 = 144\u00b0<\/p>\n

\"AP<\/p>\n

Question 5.
\nABCD is a rectangle, AC is diagonal. Find the angles of \u0394ACD. Give reasons.
\nSolution:
\n\"AP
\nGiven that \u25a1ABCD is a rectangle;
\nAC is its diagonal.
\nIn \u0394ACD; \u2220D = 90\u00b0 [ \u2235 \u2220D is also angle of the rectangle]
\n\u2220A + \u2220C = 90\u00b0 [ \u2235 \u2220D = 90\u00b0 \u21d2 \u2220A + \u2220C = 180\u00b0-90\u00b0 = 90\u00b0]
\n(i.e,,) \u2220D right angle and
\n\u2220A, \u2220C are complementary angles.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions Chapter 8 Quadrilaterals Ex 8.1 Textbook Questions and Answers. AP State Syllabus 9th Class Maths Solutions 8th Lesson Quadrilaterals Exercise 8.1 Question 1. State whether the statements are true or false. i) Every parallelogram is a trapezium. ii) All parallelograms are quadrilaterals. iii) All trapeziums are parallelograms. …<\/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\/4674"}],"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=4674"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/4674\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=4674"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=4674"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=4674"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}