Master P149 Check P161 Strengthen P163 Test P171 extend 7 Extend You will: • Extend your understanding with problem-solving. 1 The diagram shows a person walking a tightrope. The two poles are 16 m apart. The two halves of the tightrope make an angle of 10° to the horizontal. a Make a scale drawing of the triangle ABC using a ruler and protractor. Use a scale of 1 cm to 2 m. b How long is the tightrope ABC? A 10° 10° C B 16 m 2 Reasoning a Construct triangle ABC where AB = 8 cm, BC = 6 cm and AC = 7.5 cm. b Construct the perpendicular bisectors of AB and BC. Mark the point P where they cross. c Construct the perpendicular bisector of AC. What do you notice? d Draw accurately a circle with centre P and radius PC. What do you notice? e Draw another triangle ABC, this time with an obtuse angle. Repeat the steps in parts b to d. 3 Problem-solving Use a ruler and compasses to construct these angles. Check your angles using a protractor. a 15° b 105° Q3 hint How do these relate to angles you know such as 60° and 90°? 4 a Use a ruler and compasses to construct triangle ABC. A 7 cm 6 cm B 10 cm A C b Construct the perpendicular from A to the base BC. c Work out the area of the triangle. 7 cm 6 cm B 10 cm 5 Problem-solving A a Construct these two sides of triangle ABC. Join AC. 5 cm b Use your triangle to construct the quadrilateral B 6 cm ABCD where CD = 4 cm and AD = 7 cm. c Construct another quadrilateral ABCD where AB = 7.7 cm, BC = 5.2 cm, CD = 6.4 cm, AD = 7.7 cm. 167 Topic links: Polygons, 3D solids, Pythagoras’ theorem, Quadratic graphs C Q5b hint A C 7 cm D 4 cm 5 cm B 6 cm C Subject links: Science (Q16)