6 a Sketch this kite ABCD. b Split it into two congruent triangles. c Construct the kite using the method in Q5. B 6 cm 4 cm A C D 7 Problem-solving The diagram shows the penalty area of a football pitch. 40.3 m F B 9.2 m 16.5 m 11 m 2.4 m 7.3 m a Make a scale drawing of the penalty area. Use a scale of 1 cm to 4 m. b A footballer at F runs straight to the ball B on the penalty spot and kicks it towards the goal at an angle of 120° to FB. Could she score a goal? Q7b hint Draw the line and angle on your diagram. 8 Problem-solving a Draw the right-angled triangle ABC on squared paper where AB = 8 cm, BC = 6 cm and angle ABC = 90°. b Construct the perpendicular bisector of the hypotenuse AC. Mark the point P where the bisector intersects AC. c Draw the circle with centre at point P with radius PA. What do you notice? d Draw around a circular object. Use your discovery in part c to find the centre of the circle. 9 The diagram shows three sides of a regular octagon. ABP is a straight line. The length of each side is 5 cm. a Work out the marked exterior angle. b Draw accurately the sides AB and BC. c Continue in the same way to complete the octagon. Q8d Strategy hint Mark any point Q on the circumference. Construct a right-angled triangle with the right angle at P. C A B 10 Problem-solving The diagram shows a rolled-up poster inside a cardboard box. The box is a triangular prism. a Construct the triangular cross-section. b Bisect two of its angles. 8 cm 8 cm Mark the point P where the angle bisectors cross. c Bisect the third angle of the triangle. 8 cm What do you notice? d Construct a perpendicular from P onto one of the sides. Mark the point Q where it meets the side. e Draw a circle with centre P and radius PQ. f Another poster is rolled up with a diameter of 8 cm. Construct the triangular cross-section of a box for it. P 50 cm Unit 7 Constructions and loci 168