 # GCSE Maths Revision List – Geometry and Measures Foundation

Below you will find a comprehensive list of all the GCSE Maths foundation topics within Geometry and Measures you should revise. Make sure that you revise all of the GCSE Maths foundation topics and practice using the Maths Made Easy GCSE Maths Revision page where you will get access to hundreds of relevant resources.

#### Geometry and Measures:F

1. Use conventional terms and notations:

• points, lines, vertices, edges, planes
• parallel lines, perpendicular lines, right angles
• polygons, regular polygons and polygons with reflection and/or rotation symmetries
• use the standard conventions for labelling and referring to the sides and angles of triangles
• draw diagrams from written description

2. Use the standard ruler and compass constructions

• perpendicular bisector of a line segment
• constructing a perpendicular to a given line from/at a given point
• bisecting a given angle)
• use these to construct given figures and solve loci problems
• know that the perpendicular distance from a point to a line is the shortest distance to the line

3. Angles:

• Apply the properties of angles at a point
• at a point on a straight line
• vertically opposite angles
• alternate and corresponding angles on parallel lines
• derive and use the sum of angles in a triangle

4. Derive and apply the properties and definitions of:

• special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus;
• triangles and other plane figures using appropriate language

5. Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

6. Angles and Sides

• Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to find results about angles and sides
• Know that the base angles of isosceles triangle are equal
• obtain simple proofs

7. Identify, describe and construct congruent and similar shapes, including on coordinate axes,
by considering rotation, reflection, translation and enlargement (including fractional scale factors)

8. Identify and apply circle definitions and properties, including:

• centre, radius, chord, diameter, circumference
• tangent, arc, sector and segment

9. Solve geometrical problems on coordinate axes

10. Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres

11. Construct and interpret plans and elevations of 3D shapes.

12. Use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)

13. Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

14. Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)

15. Know the formulae:

• circumference of a circle = 2πr = πd, area of a circle = πr2
• calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes
• surface area and volume of spheres, pyramids, cones and composite solids

16. Calculate arc lengths, angles and areas of sectors of circles

17. Apply the concepts of congruence and similarity, including the relationships between lengths in similar figures

18. Know the formulae for: Pythagoras’ theorem, a2 + b2 = c2
… and the trigonometric ratios 19. Know the exact values of sinθ and cosθ for θ = 0°, 30°, 45° , 60° and 90°
know the exact value of tanθ for θ = 0°, 30°, 45° and 60°

20. Describe translations as 2D vectors

20. Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors;