Geometry

You will be able to

• Measure and state a three-figure bearing clockwise from north at the point the bearing is measured from.
• Calculate a back bearing by adding or subtracting 180°, and convert between map distances and real distances using a scale or map ratio.
• Determine the distance and bearing back to the start of a two-leg journey from a scale drawing or by calculation.

You will be able to

• Calculate a missing length in similar shapes, including similar triangles formed by a line parallel to one side, using the ratio of corresponding sides.
• Explain why an enlargement with length scale factor k multiplies areas by k² and volumes by k³, and use this to find areas and volumes of similar shapes and solids.
• Determine the length scale factor from a given area ratio or volume ratio by taking the square root or the cube root.

You will be able to

• Identify corresponding, alternate and co-interior angles where a transversal crosses two parallel lines.
• State that corresponding and alternate angles are equal and that co-interior angles add up to 180°, and explain why these facts need parallel lines.
• Calculate a missing angle using vertically opposite angles, angles on a straight line and angles on parallel lines, giving the reason in words.

You will be able to

• Calculate the sum of the interior angles of a polygon as (n − 2) × 180° by splitting it into triangles from one vertex.
• Explain why the exterior angles of any convex polygon add up to 360°.
• Calculate the exterior and interior angles of a regular polygon, and deduce the number of sides from either angle.

You will be able to

• State and use the angle in a semicircle and the angle between a tangent and a radius, giving the reason in exam words.
• Calculate angles using the angle at the centre (twice the angle at the circumference), angles in the same segment and opposite angles of a cyclic quadrilateral.
• Identify the alternate segment and use the alternate segment theorem to find an angle between a tangent and a chord.

You will be able to

• State that the perpendicular from the centre to a chord bisects the chord, and calculate the distance of a chord from the centre using Pythagoras' theorem.
• State that equal chords are equidistant from the centre.
• Calculate the length of the tangents from an external point, and use the kite they form with the radii (∠APB + ∠AOB = 180°) to find angles.