Similarity and congruence – Year 10 maths lesson
Lesson 11 of 37 in the Year 10 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 10 (ages 14–15) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 10 (ages 14–15)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “If you double every length of a box, what happens to its volume?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Matching the wrong sides. Match sides opposite equal angles.
- Using the length scale factor for area. Square it for area, cube it for volume.
Tip for home: Compare model cars or toys with the real thing using scale factors.
What your child will learn
We are learning to use similar and congruent shapes to find missing lengths, areas and volumes.
Success looks like
- I can show triangles are congruent.
- I can find lengths in similar shapes.
- I can use area and volume scale factors.
Key words
- congruent
- exactly the same size and shape
- similar
- same shape, different size
- scale factor
- how many times longer each length is
- corresponding
- in the same position on both shapes
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Photograph an object at two sizes and check that all lengths changed by the same factor.
The big ideas (for the adult)
Congruent shapes are identical in size and shape. Triangles are congruent by SSS, SAS, ASA or RHS.
Similar shapes have equal angles and lengths in the same ratio. The scale factor is new length ÷ old length.
For similar shapes, areas scale by the square of the length scale factor and volumes by its cube.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 10 maths lessons
- Systematic listing and counting
- Standard form
- Laws of indices
- Surds
- Fractions, decimals and recurring decimals
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Vectors
- Circle theorems
- Bearings
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Histograms
- Pie charts and time series graphs
- Scatter graphs and correlation
- Sampling
- Combined events and tree diagrams
- Simplifying expressions
- Expanding brackets
- Factorising
- Solving linear equations
- Inequalities
- Sequences and the nth term
- Straight-line graphs
- Simultaneous equations
- Quadratic equations
- Functions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
- Direct and inverse proportion
- Scale drawings and maps
- Rates of change from graphs
Curriculum
National Curriculum for England, Year 10: “apply the concepts of congruence and similarity, including the relationships between lengths, {areas and volumes} in similar figures”
GCSE subject content G19: “apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.