OCR GCSE MATHS 6.1 AND 6.2 GEOMETRICAL INSTRUMENTS,BISECTORS AND PERPENDICULARS EXAM WITH LATEST QUESTIONS AND ANSWERS A+ GRADED

Exercise 1 1 Estimate and measure the size of these angles. a b Using protractors to draw angles WORKED EXAMPLE Use a protractor to draw ∠ABC = 76°. Solution Draw a horizontal line using your ruler. Mark a point on the line and label it B. Place the centre of the protractor exactly on B. Be careful! When choosing which scale to use on your protractor, remember that 76° is an acute angle. Mark 76° with a pencil. Remove the protractor and draw a line from B through the 76° marking, using a ruler. Label the angle correctly. 2 Use a ruler and protractor to draw and label these angles. a 65° b 150° c 210° d 330° Reminder Construct means to draw shapes, angles or lines accurately. 6.1 AND 6.2 GEOMETRICAL INSTRUMENTS, BISECTORS AND PERPENDICULARS ©Cambridge University Press and OCR 2021 3 3 Using a ruler and protractor only, construct the following triangles. None of the diagrams are drawn to scale. a b c Using compasses to construct circles 4 Use compasses to construct: a a circle of radius 4cm b a circle of diameter 12cm c a circle of diameter 6cm that shares a centre, O, with another circle of radius 5cm 5 a Using compasses, draw a circle of radius 3.5cm and centre O. b Use a ruler to draw any two radii of the circle. Label them OA and OB. c Join point A to point B to form triangle AOB. d Measure angles AOB, OBA and BAO. Write the measurements on your diagram. 6.2 Bisectors and perpendiculars Read the following worked examples that use a ruler and compasses only, then practise the constructions yourself. Never rub out any construction arcs you draw. WORKED EXAMPLE Bisecting a line segment (bisect means to divide exactly in two). Place the point of your compasses on A. Open your compasses to any length greater than half the length of AB. Draw arcs above and below the line. Keeping your compasses open to the same width, place the point on B. Draw arcs above and below the line so that they intersect the first set of arcs. Use a ruler to join the points where the arcs intersect. This is the bisector of the line segment AB.