## Developing Geometry

## Overview

Learners will extend their knowledge and understanding of angle facts from Year 7 and solve increasingly complex angle problems. Links are then make to the connected properties of polygons and quadrilaterals. Learners will also learn about further constructions with pairs of compasses.

Following this learners will consolidate their understanding of how to find the area of trapezia from Year 7 and extend this to include circles and common sectors. A key aspect of this half term is for learners to be able to choose and use correct formulae reinforcing shapes the names of shapes and their properties.

Transforming shapes by reflection and understanding line symmetry and rotational symmetry is developed at the end of this half term. Here learners can also revisit and enhance their knowledge of types of triangles and quadrilaterals. Please note: rotation and translation are not introduced at this point to enable students to attain a deeper understanding and avoid mixing up the different concepts.

## Building on

Angles in Parallel Lines (Year 7 Summer 1)

Constructing Triangles (Year 7 Summer 1)

Perimeter of shapes (Year 7 Spring 1)

Area of Trapezia & Parallelograms (Year 7 Spring 1)

Rounding (Year 7 Autumn 2)

Plotting linear graphs (Year 8 Autumn 2)

## Powerful Knowledge

Derive and use the angle sum in any polygon

Derive and use the angle sum of exterior angles of any polygon

Understand properties of triangles, quadrilaterals and circles

Use compasses to construct bisectors

Derive and apply formulae for area and circumference of a circle

Recognise line symmetry

Reflect shapes in vertical, horizontal and diagonal lines

Describe rotational symmetry

## Lesson Resources

**Angles in Polygons**

Lesson 1 – Interior angles of polygons

Lesson 2 – Exterior angles of polygons

Lesson 3 – Solving polygon problems

Lesson 4 – Constructing polygons

**Area and Perimeter of Circles **

Lesson 6 – Constructing an angle bisector

Lesson 7 – Constructing a perpendicular bisector

Lesson 8 – Circumference of a circle

Lesson 9 – Circumference problems

Lesson 11 – Area of compound shapes

Lesson 12 – Further area and perimeter problems

**Symmetry and Reflection**

Lesson 13 – Reflecting shapes on a coordinate grid

Lesson 15 – Rotational symmetry

Updated July 2024