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Grade 7 Mathematics: Geometry Polygons and Circles Question 1: Multiple Choice (5) 1.1 Which one of the following statements is FALSE? A A right-angled triangle cannot have an obtuse angle. B All squares are rectangles. C Co-interior angles are always equal. D All rectangles are parallelograms. 1.2 Which polygons fit the following description? Two opposite angles are equal, diagonals bisect at a right angle. A rhombus and parallelogram B rhombus and a square C rectangle and parallelogram D square and rectangle 1.3 A closed shape with seven sides, not all equal, is a/an: A irregular heptagon B irregular hexagon C regular heptagon D regular hexagon 1.4 Which two shapes will be formed if one diagonal line is drawn inside a square? A equilateral triangles B acute-angled triangles B right-angled scalene triangles D right-angled isosceles triangles 1.5 Which of the following describes an isosceles trapezium? A Two pairs of parallel and equal sides B One pair of parallel sides and another pair of equal sides C One pair of parallel and equal sides D Two pairs of parallel sides and one pair of equal angles Question 2: Match Column A to Column B Column A Answer (8) Column B 2.1 congruent triangles A Two pairs of parallel sides, opposite angles equal 2.2 kite B No angles or sides are equal 2.3 pentagon C Angles are equal, length of sides are different 2.4 similar triangles D Angle greater than 1800 2.5 trapezium E Corresponding angles and sides are equal 2.6 scalene triangle F Interior angles measuring 1080 each 2.7 parallelogram G Diagonals cross at a 900 angle 2.8 reflex angle H One pair of parallel sides Page 1 of 13 Grade 7 Mathematics: Geometry Polygons and Circles Question 3: Construct and name the following angles. 3.1 ∠ABC = 2980 Question 4: 3.2 (4) ∠DEF = 1150 Circles 4.1 Construct a circle with a diameter of 5cm. (2) 4.2 Draw in a radius, separate from the diameter and show the measurement. (1) 4.3 Draw and label a chord. (1) 4.4 What is the section between the two radii called? 4.5 What is the difference between a radius and a chord? _____________________ (1) (2) ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 4.5 Use a green pen to show the circumference. Page 2 of 13 Grade 7 Mathematics: Geometry Polygons and Circles > Question 5: Constructing polygons Draw line segment AB = 6 cm. Construct line BC = 4 cm, with ABC = 650. Construct line > 5.1.1 CD ll AB, where CD = 6 cm and BCD = 1150. Connect point D and A.(Remember to show all symbols and measurements) (6) Classify shape ABCD _________________________________ 5.2.1 Construct polygon EFGH, where line EF = FG = 30 mm and EFG = 750. Draw line (1) > > > 5.1.2 GH = EH = 50 mm and FEH = FGH = 1200. Connect point E to point G with a straight line. Construct a perpendicular bisector of line EG, through point I, connecting point F and H. (7) Page 3 of 13 Grade 7 Mathematics: Geometry Polygons and Circles 5.2.2 Classify polygon EFGH. ________________________________________ (1) 5.2.3 Classify △EFI ________________________________________ (2) 5.2.4 Classify △EFG ________________________________________ (1) 5.2.5 Calculate the size of ∠FGE , with a reason. (2) _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Question 6: Calculate the value of the angles, with reasons, as requested: 6.1 Calculate the values of x and y: (4) _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Page 4 of 13 Grade 7 Mathematics: Geometry Polygons and Circles 6.2 ABCD is a parallellogram. Calculate the value of w, x, y, z : _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Page 5 of 13 Mathematics: Geometry 6.3 Grade 7 Find the values of all the variables: _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Question 7: Perimeter 7.1 A number of identical circles are tightly packed inside a rectangle. The radius of one circle is 3,5 metres. What is the perimeter of the rectangle into which the circles are packed? (3) ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ _____________________________________________________________________________ Page 6 of 13 Grade 7 Mathematics: Geometry Polygons and Circles 7.2.1 Find the value of x , if the perimeter of the shape is 44,5 cm: (3) ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 7.2.2 Give the perimeter in metres. ________________________________________ (1) 7.2.3 Classify the polygon. ________________________________________ (1) 7.3 There are six identical squares in this shape. The perimeter of one square is 1 800 cm. 7.3.1 Find the perimeter of the shape. (2) ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ 7.3.2 Give the perimeter in kilometres. (1) ___________________________________________ 7.3.3 Which 3-D shape will be formed if this shape is folded? (1) ___________________________________________ Page 7 of 13 Grade 7 Mathematics: Geometry MEMO: Question 1: Multiple Choice (5) 1.1 Which one of the following statements is FALSE? A A right-angled triangle cannot have an obtuse angle. B All squares are rectangles. C Co-interior angles are always equal. (Co-interior angles add up to 1800) D All rectangles are parallelograms. 1.2 Which polygons fit the following description? Two opposite angles are equal, diagonals bisect at a right angle. A rhombus and parallelogram B rhombus and a square C rectangle and parallelogram D square and rectangle 1.3 A closed shape with seven sides, not all equal, is a/an: A irregular heptagon B irregular hexagon C regular heptagon D regular hexagon 1.4 Which two shapes will be formed if one diagonal line is drawn inside a square? A equilateral triangles B acute-angled triangles B right-angled scalene triangles D right-angled isosceles triangles 1.5 Which of the following describes an isosceles trapezium? A Two pairs of parallel and equal sides B One pair of parallel sides and another pair of equal sides C One pair of parallel and equal sides D Two pairs of parallel sides and one pair of equal angles Question 2: Math Column A to Column B (8) Column A Answer Column B 2.1 congruent triangles E A Two pairs of parallel sides, opposite angles equal 2.2 kite G B No angles or sides are equal 2.3 pentagon F C Angles are equal, length of sides are different 2.4 similar triangles C D Angle greater than 1800 2.5 trapezium H E Corresponding angles and sides are equal 2.6 scalene triangle B F Interior angles measuring 1080 each 2.7 parallelogram A G Diagonals cross at a 900 angle 2.8 reflex angle D H One pair of parallel sides Page 8 of 13 Grade 7 Mathematics: Geometry Question 3: Construct and name the following angles. 3.1 ∠ABC = 2980 3.2 (4) ∠DEF = 1150 620 Reflex angle (Remember when constructing a reflex angle use 3600 - angle, then measure the acute angle first) Question 4: Obtuse angle Circles 4.1 Construct a circle with a diameter of 5cm. (2) 4.2 Draw in a radius, separate from the diameter and show the measurement. (1) 4.3 Draw and label a chord. (1) 4.4 What is the section between the two radii called? 4.5 What is the difference between a radius and a chord? Sector (1) (2) A radius is the straight line from the centre of the circle to any point on the circumference. A chord is a straight line connecting any two points on the circumference of a circle, but not through the centre of the circle. 4.5 Use a green pen to show the circumference. (1) Page 9 of 13 Grade 7 Mathematics: Geometry > Question 5: Constructing polygons Draw line segment AB = 6 cm. Construct line BC = 4 cm, with ABC = 650. Construct line > 5.1.1 CD ll AB, where CD = 6 cm and BCD = 1150. Connect point D and A.(Remember to show all symbols and measurements) (6) (Not drawn to scale, remember all symbols and measurements) Classify shape ABCD Parallelogram (1) 5.2 Construct polygon EFGH, where line EF = FG = 30 mm and EFG = 750. Draw line > > > 5.1.2 GH = EH = 50 mm and FEH = FGH = 1200. Connect point E to point G with a straight line. Construct a perpendicular bisector of line EG at point I , connecting point F and H. (7) (Not drawn to scale, remember all symbols and measurements) I Page 10 of 13 Grade 7 Mathematics: Geometry 5.2.2 Classify polygon EFGH. kite (1) 5.2.3 Classify △EFI right-angled scalene triangle (2) 5.2.4 Classify △EFG isosceles triangle (1) 5.2.5 Calculate the size of ∠FGE , with a reason. ∠FGE = (180° − 75°) ÷ 2 ∠FGE = 52,5° (1) Two angles of an isosceles triangle is equal. Question 6: Calculate the value of the angles, with reasons, as requested: 6.1 Calculate the values of x and y. (4) 600 220 1200 600 600 TIP: Write everything you know onto the drawing, e.g. equilateral triangle - all angles equal 600 before you start. Then write each angle you solve onto the drawing. Supplementary angles equal 1800 ∠DBC = 180° − 158° = 22° Equilateral triangle - All angles are equal to 600 ∠CDE = 60° Supplementary angles equal 1800 x = 180° − 60° = 120° y = 180° − 120° − 22° = 38° Inner angles of a triangle add up to 1800 6.2 w, x, y, z : ABCD is a parallellogram. Calculate the value of (4) >> >>> >>> 450 600 >> 450 First add in everything you know! w = 180° − (90° + 45°) = 45° Inner angles of a triangle add up to 1800 z = 45° ∠BHA = 90° y = 180° − (90° + 30°) = 60° Alternate angles are equal x = 60° Opposite angles of a parallellogram is equal Supplementary angles add up 1800 Inner angles of a triangle add up to 1800 Page 11 of 13 Grade 7 Mathematics: Geometry 6.3 Find the value of all the variables: (7) b = 85° Vertically opposite angles f = 85° Coordinating angles d = 85° Vertically opposite angles h = 180° − 85° = 95° Co-interior angles a = 95° Alternate angles g = 95° Coordinating angles e = 95° Alternate angles There may be more than one way to get to the answers. Remember: No reason, no mark! Question 7: Perimeter 7.1 A number of identical circles are tightly packed inside a rectangle. The radius of one circle is 3,5 metres. What is the perimeter of the rectangle into which the circles are packed? (3) Diameter of one circle: 3,5 m x 2 = 7 m Length of rectangle = 7 m x 5 = 35 m Breadth of rectangle = 7 m x 3 = 21 m Perimeter = 2ℓ + 2b = (2 x 35 m) + (2 x 21 m) = 112 metres Page 12 of 13 Grade 7 Mathematics: Geometry 7.2.1 Find the value of x , if the perimeter of the shape is 44,5 cm: (3) x + x + 2x + 7, 3cm + 9cm + 3cm + 8, 4cm = 44,5cm 4x + 30,9 = 44,5cm 4x = 13,6cm x = 3, 4cm 7.2.2 Give the perimeter in metres. 44,5 cm = 0,445m (1) 7.2.3 Classify the polygon. Irregular octagon (1) 7.3 There are six identical squares in this shape. The perimeter of one square is 1 800 cm. 7.3.1 Find the perimeter of the shape. (2) One side of the square = 1800cm ÷ 4 = 450cm Perimeter = 14 × 450cm = 6300cm 7.3.2 Give the perimeter in kilometres. (1) 6 300 cm = 63 m = 0,063 km 7.3.3 Which 3-D shape will be formed if this shape is folded? (1) A cube Page 13 of 13