Good Learning Co.
SavannahYear 8
← Maths
MathsAngles, congruence and similarity30 min★★★ difficulty

Congruence and enlargement

Congruent means identical; similar means the same shape at a different size. Knowing which one a question is about decides whether you compare lengths or scale them.

Lesson overview

What you'll learn in this lesson

Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

Key learning points

  • • The four congruence conditions
  • • Why SSA is not enough
  • • Enlarging by a scale factor
  • • Similar shapes and missing lengths

This lesson at a glance

  • 30 minutes
  • 19 parts to scroll through
  • 4 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

constructcongruenttrianglessimilarshapes

Scroll down — the lesson carries on below

Part 1 of 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Congruence and enlargement

An English teaching video on this topic from SHFT - Your Learning. Watch it, then scroll down for the lesson.

In a nutshell

Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

2

What you already know

Part 2 of 19

Before we start

What you already know

You can construct triangles with a ruler and protractor and plot coordinates.

Recap: Angle sums in triangles and polygons
3

Key words

Part 3 of 19

Key words

Words you'll need today

congruent
Exactly the same shape and size, possibly rotated or reflected.
similar
The same shape, with all lengths in the same ratio.
centre of enlargement
The fixed point from which an enlargement is measured.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Part 1 — Congruent triangles

A short piece of teaching, then a check to make sure it has landed.

5

Explore the idea

Part 5 of 19

Learn

The four congruence conditions

Two triangles are congruent if they match by SSS (three sides), SAS (two sides and the angle between them), ASA (two angles and a corresponding side) or RHS (right angle, hypotenuse, one side). Naming the condition is what earns the mark in a proof.

6

Explore the idea

Part 6 of 19

Learn

Why SSA is not enough

Two sides and a non-included angle can produce two genuinely different triangles, so SSA does not prove congruence. AAA does not either — it fixes the shape but not the size, which is exactly what similarity means. These two near-misses are the ones examiners test.

7

Quick check

Part 7 of 19

Quick check

Which does NOT prove congruence?

8

Quick check

Part 8 of 19

Quick check

Enlargement scale factor 4: a 3 cm side becomes...

9

Reset break

Part 9 of 19

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
10

Learning cycle

Part 10 of 19

Learning cycle 2 of 2

Part 2 — Enlargement and similarity

A short piece of teaching, then a check to make sure it has landed.

11

Explore the idea

Part 11 of 19

Learn

Enlarging by a scale factor

An enlargement scale factor 3 from a centre triples every distance from the centre. A point 2 squares right and 1 up from the centre moves to 6 right and 3 up. Angles stay the same, so the image is similar to the object. Scale factor 1/2 makes the image smaller — still called an enlargement in maths.

12

Explore the idea

Part 12 of 19

Learn

Similar shapes and missing lengths

In similar shapes, matching lengths share one scale factor. If a triangle with sides 4 cm and 6 cm is similar to one whose matching 4 cm side is 10 cm, the scale factor is 2.5 and the other side is 15 cm. Find the scale factor from a known pair first, then apply it — never add the difference.

13

Quick check

Part 13 of 19

Quick check

Under enlargement, angles...

14

Quick check

Part 14 of 19

Quick check

Similar triangles: 5 cm matches 12.5 cm. Scale factor?

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Believing SSA or AAA proves congruence.
  • Adding the difference in lengths instead of multiplying by a scale factor.
  • Forgetting that a fractional scale factor still counts as an enlargement.
16

Challenge round

Part 16 of 19

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

17

Challenge round

Part 17 of 19

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Two triangles are ____ if they match by SSS (three sides), SAS (two sides and the angle between them), ASA (two angles and a corresponding side) or RHS (right angle, hypotenuse, one side).

Two sides and a non-included angle can produce two genuinely different ____, so SSA does not prove congruence.

Angles stay the same, so the image is ____ to the object.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Congruence and enlargement

6 questions, marked with the reasoning shown. No timer.

  1. 1. Congruent shapes have...

  2. 2. Which condition uses a right angle?

  3. 3. Scale factor 1/3: a 9 cm side becomes...

  4. 4. Similar shapes always have equal...

  5. 5. Scale factor 2 doubles distances from the...

  6. 6. Triangle sides 3, 4, 5 and 9, 12, 15 are...

19

Lesson round-up

Part 19 of 19

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 19 · Watch & discover

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