{"id":10511,"date":"2021-04-16T18:22:21","date_gmt":"2021-04-16T12:52:21","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=10511"},"modified":"2021-09-15T11:33:36","modified_gmt":"2021-09-15T06:03:36","slug":"ap-board-7th-class-maths-solutions-chapter-12-ex-2","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-7th-class-maths-solutions-chapter-12-ex-2\/","title":{"rendered":"AP Board 7th Class Maths Solutions Chapter 12 Quadrilaterals Ex 2"},"content":{"rendered":"

AP State Syllabus AP Board 7th Class Maths Solutions<\/a> Chapter 12 Quadrilaterals Ex 2 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 7th Class Maths Solutions 12th Lesson Quadrilaterals Exercise 2<\/h2>\n

\"AP<\/p>\n

Question 1.
\nState whether true or false
\n(i) All rectangles are squares ( )
\n(ii) All rhombuses are parallelogram ( )
\n(iii) All squares arc rhombuses and also rectangles ( )
\n(iv) All squares are not parallelograms ( )
\n(v) All kites arc rhombuses ( )
\n(vi) All rhombuses are kites ( )
\n(vii) All parallelograms are trapeziums ( )
\n(viii) All squares are trapeziums ( )
\nSolution:
\n(i) All rectangles are squares ( False)
\n(ii) All rhombuses are parallelogram ( True)
\n(iii) All squares arc rhombuses and also rectangles ( True)
\n(iv) All squares are not parallelograms (False )
\n(v) All kites arc rhombuses ( False)
\n(vi) All rhombuses are kites (True )
\n(vii) All parallelograms are trapeziums ( True)
\n(viii) All squares are trapeziums ( True)<\/p>\n

Question 2.
\nExplain how a square is a
\n(i) quadrilateral
\n(ii) parallelogram
\n(iii) rhombus
\n(iv) rectangle.
\nSolution:
\ni) quadrilateral : A square is a closed figure bounded by four line segments and hence it is a
\nquadrilateral.
\nii) Parallelogram : In a square both pairs of opposite sides are parallel and hence it is a parallelogram.
\niii) Rhombus : All four sides of a square are equal, thus it is a Rhombus.
\niv) Rectangle : In a square each angle \u00a1s a right angle and hence it is a rectangle.<\/p>\n

Question 3.
\nIn a rhombus ABCD, \u2220CBA = 40\u00b0.
\nFind the other angles.
\n\"AP
\nGiven that \u2220CBA , \u2220B = 40\u00b0
\nWe know that rhombus is a parallelogram and
\nadjacent angles are supplementary.
\nThus \u2220A + \u2220B = 180\u00b0
\n\u2220A + 40\u00b0 = 180\u00b0
\n\u2220A = 180\u00b0 – 40\u00b0 = 140\u00b0
\nAlso opposite angles are equal.
\n\u2234 \u2220A =\u2220C = 140\u00b0
\n\u2220D = \u2220B = 40\u00b0<\/p>\n

\"AP<\/p>\n

Question 4.
\nThe adjacent angels of a parallelogram arex\u00b0 and (2x + 30)\u00b0.
\nFind all the angles of the parallelogram.
\nSolution:
\n\"AP
\nGiven that the adjacent angles of a parallelogram are x\u00b0 ; (2x + 30)\u00b0
\nAdjacent angles of a parallelogram are supplementary.
\n\u2234 x + (2x + 30) = 180\u00b0
\n3x + 30 = 180\u00b0
\n3x = 180\u00b0 – 30\u00b0 = 150\u00b0
\nx = \\(\\frac{150^{\\circ}}{3}\\) = 50\u00b0
\n\u2234 The adjacent angles are x = 50\u00b0
\n2x + 30\u00b0= 2 x 50 + 30 = 130\u00b0
\n\u2234 The other two angles are 50\u00b0, 130\u00b0
\n\u2234 The four angles are 50\u00b0, 130\u00b0, 50\u00b0, 130\u00b0<\/p>\n

Question 5.
\nExplain how DEAR is a trapezium. Which of its two sides are parallel?
\nSolution:
\n\"AP
\nIn quadrilateral DEAR
\n\u2220D = 80\u00b0 and \u2220E = 100\u00b0
\nAlso \u2220D + \u2220E = 80\u00b0+ 100\u00b0 = 180\u00b0
\n(\u2235 D, E are interior angles on the same side of \\(\\overline{\\mathrm{DE}}\\))
\n\u2234 DR \/\/EA
\nAlso \u2220A = \u2220R = 90\u00b0 and \u2220A + \u2220R = 180\u00b0
\n\u2234 DEAR is a trapezium.<\/p>\n

\"AP<\/p>\n

Question 6.
\nBASE is a rectangle. Its diagonals intersect atO. Findx, if OB = 5x+1 and OE = 2x + 4.
\nSolution:
\n\"AP
\nGiven BASE is a rectangle.
\nOB = 5x + 1 and OA = 2x + 4
\nIn a rectangle diagonals are equal.
\nBS = EA
\n(i.e.) 2 x BO = 2 x OA
\n2(5x + 1) = 2(2x + 4 )
\n10x + 2 = 4x + 8
\n10x – 4x = 8 – 2
\n6x = 6
\nx = 1<\/p>\n

Question 7.
\nIs quadrilateral ABCD a parallelogram, if \u2220A = 70\u00b0 and \u2220C = 65\u00b0 ? Give reason.
\nSolution:
\nGiven that in quadrilateral ABCD, \u2220A = 70\u00b0 and \u2220C = 65\u00b0
\n\u2220A and \u2220C are opposite angles and are not equal.
\nHence quadrilateral ABCD is not a parallelogram.<\/p>\n

\"AP<\/p>\n

Question 8.
\nTwo adjacent sides of a parallelogram are in the ratio 5:3 the perimeter of the parallelogram is 48cm. Find the length of each of its sides.
\nSolution:
\nGiven that the ratio of two adjacent sides of a parallelogram = 5 : 3
\nSum of the terms of the ratio = 5 + 3 = 8
\nSum of two sides = half of the perimeter = \\(\\frac { 1 }{ 2 }\\) x 48 = 24 cm
\n\u2234 one side = \\(\\frac { 5 }{ 8 }\\) x 24 = 15 cm
\nother side = \\(\\frac { 3 }{ 8 }\\) x 24 = 9 cm
\n\u2234 The four sides are 15 cm, 9 cm, 15 cm, 9 cm ( opposite sides are equal)<\/p>\n

Question 9.
\nThe diagonals of the quadrilateral are perpendicular to each other. Is such a quadrilateral
\nalways a rhombus? Draw a rough figure to justify your answer.
\nSolution:
\n\"AP
\nGiven : Diagonals are perpendicular.
\nIf the diagonals are perpendicular then the
\nquadrilateral need not necessarily be a rhombus.
\nLook at the figure,
\nthe diagonals are perpendicular to each other.
\nBut all the sides are not equal.
\nPR \u22a5 QS but PQ \u2260 QR \u2260 RS \u2260 SP<\/p>\n

\"AP<\/p>\n

Question 10.
\nABCD is a trapezium in which \\(\\overline{\\mathrm{AB}} \\| \\overline{\\mathrm{DC}}\\) If \u2220A = \u2220B =30\u00b0, what are the measures of the other two angles?
\nSolution:
\n\"AP
\nGiven : ABCD is a trapezium.
\n\u2220A = \u2220B = 30\u00b0
\nSince AB\/\/CD,
\n\u2220A + \u2220D = \u2220B + \u2220C = 180\u00b0 (interior angles on the same side of a
\ntransversal are supplementary)
\n30\u00b0 + \u2220D = 180\u00b0
\n\u2220D = 180\u00b0 – 300\u00b0
\n= 150\u00b0
\nand 30\u00b0 + \u2220C = 180\u00b0
\n\u2220C = 180\u00b0 – 30\u2019
\n= 150\u00b0<\/p>\n

\"AP<\/p>\n

Question 11.
\nFill in the blanks.
\n(i) A parallelogram in which two adjacent sides are equal is a ………………….
\n(ii) A parallelogram in which one angle is 90\u00b0 and two adjacent sides are equal is a ………………….
\n(iii) IntrapeziurnABCD,\\(\\overline{\\mathrm{AB}} \\| \\overline{\\mathrm{DC}}\\) . If \u2220D = x\u00b0 then \u2220A = ………………
\n(iv) Every diagonal in a parallelogram divides it into …………………. triangles.
\n(v) In parallelogram ABCD, its diagonals \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{BD}}\\) intersect atO. IfAO = 5cm then AC = …………….. cm.
\n(vi) In a rhombus ABCD, its diagonals intersect at \u2018O\u2019. Then \u2220AOB = …………. degrees.
\n(vii) ABCD is a parallelogram then \u2220A \u2014 \u2220C = ………………… degrees.
\n(viii) In a rectangle ABCD, the diagonal AC =10cm then the diagonal BD = …………… cm.
\n(ix) In a square ABCD, the diagonal \\(\\overline{\\mathrm{AC}}\\) is drawn. Then \u2220BAC = …………
\nSolution:
\n(i) A parallelogram in which two adjacent sides are equal is a rhombus<\/span>
\n(ii) A parallelogram in which one angle is 90\u00b0 and two adjacent sides are equal is a square<\/span>
\n(iii) IntrapeziurnABCD,\\(\\overline{\\mathrm{AB}} \\| \\overline{\\mathrm{DC}}\\) . If \u2220D = x\u00b0 then \u2220A = 180\u00b0 – x<\/span>
\n(iv) Every diagonal in a parallelogram divides it into two congruent<\/span> triangles.
\n(v) In parallelogram ABCD, its diagonals \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{BD}}\\) intersect atO. If AO = 5cm then AC = 10<\/span> cm.
\n(vi) In a rhombus ABCD, its diagonals intersect at \u2018O\u2019. Then \u2220AOB = 90\u00b0<\/span>
\n(vii) ABCD is a parallelogram then \u2220A \u2014 \u2220C = zero<\/span> degrees.
\n(viii) In a rectangle ABCD, the diagonal AC =10cm then the diagonal BD = 10<\/span> cm.
\n(ix) In a square ABCD, the diagonal \\(\\overline{\\mathrm{AC}}\\) is drawn. Then \u2220BAC = 45\u00b0\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus AP Board 7th Class Maths Solutions Chapter 12 Quadrilaterals Ex 2 Textbook Questions and Answers. AP State Syllabus 7th Class Maths Solutions 12th Lesson Quadrilaterals Exercise 2 Question 1. State whether true or false (i) All rectangles are squares ( ) (ii) All rhombuses are parallelogram ( ) (iii) All squares arc …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[9],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/10511"}],"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=10511"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/10511\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=10511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=10511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=10511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}