Core Geometry

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Sample objectives

What this unit covers

• Geometrical terms: 1 Recognize and understand the following geometrical terms: point, vertex, line, parallel, perpendicular, bearing, right angle, acute, obtuse, reflex angles, interior and exterior angles, similar, congruent, and scale factor. 2 Understand and use the vocabulary related to: Triangles (equilateral, isosceles, scalene, right-angled), special quadrilaterals (square, rectangle, kite, rhombus, parallelogram, trapezium), polygons (regular and irregular polygons, pentagon, hexagon, octagon, decagon), and simple solids (cube, cuboid, prism, cylinder, pyramid, cone, sphere; the term 'hemisphere' is not required). 3 Understand and use the vocabulary associated with circles, including centre, radius (plural: radii), diameter, circumference, semicircle, chord, tangent, arc, sector, and segment.
• Geometrical constructions: 1. Use a ruler to measure and draw straight lines and angles. Note that constructing perpendicular bisectors and angle bisectors is not necessary. 2. Create a triangle when given the lengths of all sides, using only a ruler and compass. Ensure that construction arcs are included. 3. Draw, utilize, and interpret nets, such as those for cubes, cuboids, prisms, and pyramids, and apply measurements from these nets to find volumes and surface areas.
• Scale drawings: Create and understand scale drawings using a ruler for straight lines. Interpret three-figure bearings, which are measured clockwise from north (000° to 360°). For example, determine the bearing of point A from point B if the bearing of point B from point A is 025°. This includes knowledge of the directions north, east, south, and west, such as identifying that point D is directly east of point C.
• Similarity: Determine the lengths of shapes that are similar to one another.
• Symmetry: Identify line symmetry and the order of rotational symmetry, including the characteristics of triangles, quadrilaterals, and two-dimensional shapes related to their symmetries.
• Angles: 1. Determine unknown angles and provide basic explanations using these geometric properties: the total of angles around a point is 360°, the total of angles on a straight line is 180°, vertically opposite angles are equal, the angle sum in a triangle is 180°, and in a quadrilateral is 360°. 2. Find unknown angles and explain geometrically the angles created by parallel lines: corresponding angles are equal, alternate angles are equal, and co-interior angles add up to 180° (supplementary). 3. Understand and apply the angle properties of regular polygons, including both exterior and interior angles, as well as the angle sum.
• Circle theorems: Understand and apply circle theorems to find unknown angles and provide explanations. You should use the following properties of circles when justifying your answers: the angle in a semicircle is 90 degrees, and the angle between a tangent and a radius is also 90 degrees.