Geometry

Geometry is the maths of shape, size and position. Builders, designers and surveyors use it every day: to check that a frame is square, to make parts that fit exactly, or to measure a river without crossing it. In Year 7 you learned the angle facts for parallel lines and triangles and moved shapes with translations, reflections and rotations. In this topic you'll find out exactly when two shapes are copies of each other (congruent) or enlargements of each other (similar), learn the tests that prove it for triangles, and use those tests to explain why quadrilaterals have the properties they do.

What you'll learn

• 7.01 Angles and triangles: the angle sum, exterior angles, isosceles triangles, and which side lengths can make a triangle.
• 7.02 Transformations and congruence: congruent figures, describing translations, reflections and rotations exactly, and matching sides and angles.
• 7.03 Congruent triangles: the tests SSS, SAS, AAS and RHS, writing congruence statements, and simple proofs.
• 7.04 Transformations and similarity: enlargements from a centre, scale factors, and finding unknown sides in similar figures.
• 7.05 Similar triangles: the similarity tests, nested and crossed triangles, and measuring heights with shadows and mirrors.
• Investigation: determine congruence or similarity. Follow, design and test algorithms (flowcharts and step-by-step rules) that decide whether two shapes are congruent, similar or neither.
• 7.06 Properties of quadrilaterals: sides, angles and diagonals of the special quadrilaterals, and proving these properties with congruent triangles.
• Investigation: 3D coordinate systems. Use (x, y, z) coordinates to locate points in a room and a box, and explore them with 3D software.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: simpler diagrams and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: algebra, multi-step problems and written proofs, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.