GEOMETRY AND MEASURES:H

**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 and negative scale factors**

**8. Describe the changes and invariance achieved by combinations of rotations, reflections and translations**

**9. Identify and apply circle definitions and properties, including:**

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

**10. Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results**

**11. Solve geometrical problems on coordinate axes**

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

**13. Construct and interpret plans and elevations of 3D shapes.**

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

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

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

**17. Know the formulae:**

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

** **

**18. Calculate arc lengths, angles and areas of sectors of circles**

**19. Apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures**

**20. Know the formulae for: Pythagoras’ theorem, a ^{2} + b^{2} = c^{2}**

… and the trigonometric ratios

apply them to find angles and lengths in right-angled triangles and, **where possible, general triangles **in two and **three** dimensional figures

**21. 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°

**22. Know and apply the sine and cosine rule**

and a^{2} = b^{2} + c^{2} – 2bcCosA

to find unknown lengths and angles

**23. Know and apply : Area triangle = ½absinC **

to calculate the area, sides or angles of any triangle.

**24. Describe translations as 2D vectors**

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

** use vectors to construct geometric arguments and proofs**