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Hill Gate School, New Colony - |, Class - VIII, 2022 Mathematics Note - III, Chapter - 3: Understanding Quadrilaterals, Exercise 3.1 Page: 41, 1., Given here are some figures., (1), (3), (5), (6), (7), (8), Classify each of them on the basis of the following., (a) Simple curve, (b) Simple closed curve, (c) Polygon, (d) Convex polygon, (e) Concave polygon, Solution: (a) Simple curve: 1, 2, 5, 6 and 7, (b) Simple closed curve: 1, 2, 5, 6 and 7, (c) Polygon: 1 and 2, (d), Convex polygon: 2, (e), Concave polygon: 1, 2., How many diagonals does each of the following have?, (a), A convex quadrilateral, (b) A regular hexagon, (c) A triangle
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Solution: (a), A convex quadrilateral: 2., (b), A regular hexagon: 9., (c), A triangle: 0, 5., What is a regular polygon?, State the name of a regular polygon of, (i) 3 sides (ii) 4 sides (iii) 6 sides, Solution: Regular polygon: A polygon having sides of equal length and, angles of equal measures is called regular, polygon. i.e., A regular polygon is both, equilateral and equiangular., (i), A regular polygon of 3 sides is called equilateral triangle., (ii), A regular polygon of 4 sides is called square., (iii) A regular polygon of 6 sides is called regular hexagon., 6., Find the angle measure x in the following figures.
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50°, 70°, 130°, 120°, 60°, (a), (b), 30, 70°, 60°, (c), (d), Solution: (a), The figure is having 4 sides. Hence, it is a quadrilateral., Sum of angles of the quadrilateral = 360°, 50° + 130° + 120° + x = 360°, → 300° + x = 360°, → X= 360° - 300° = 60°, (b), → 90° + 70° + 60° + x = 360°, → 220° + x = 360°, → X= 360° - 220° = 140°, (c), The figure is having 5 sides. Hence, it is a pentagon., 300, 70° 110 120, 60°
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Sum of angles of the pentagon = 540°, %3D, Two angles at the bottom are linear pair., 180° - 70° = 110°, 180° – 60° = 120°, → 30° + 110° + 120° + x+ x = 540°, - 260° + 2x = 540°, - 2x = 540° - 260°, = 280°, - 2x = 280°, 280°, 2, .: X = 140°, (d) The figure is having 5 equal sides. Hence, it is a regular, pentagon. Thus, its all angles are equal., 5x = 540°, → X = 540°/5, → X = 108°, 7., 90°, EX30°, 80°, 120A, (a) Find x+y+z, (b) Find x+ y+z+w, Solution: (a), z+ 30° = 180°, (Linear pair), %3D, - Z = 180° – 30°, = 150°, And. x+ 90° = 180°, (Linear pair), %3D
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- X= 180° – 90°, = 90°, Sum of all angles of triangle = 180°, %3D, One side of triangle = 180°- (90° + 30°) = 60°, %3D, %3D, y+ 60° = 180°, (Linear pair), y = 180° – 60° = 120°, Thus, x+ y+ z = 90° + 120° + 150°, = 360°, Exercise 3.3 Page: 50, 1., Given a parallelogram ABCD. Complete each statement along, with the definition or property used., (1), AD = ...., (ii), ZDCB =, (iii) oC =, (iv), m ZDAB + m 2CDA =, Solution: (i), AD = BC (Opposite sides of a parallelogram are equal), (ii), ZDCB = ZDAB (Opposite angles of a parallelogram are, equal), (iii) OC = OA (Diagonals of a parallelogram are equal), (iv), m ZDAB + m ZCDA = 180°, %3D, 2., Consider the following parallelograms. Find the values of the, unknown x, y, z
