G8GeometryFoundation & Higher

Similarity & Congruence

Two shapes are congruent if they are identical (same size and shape), and similar if one is an enlargement of the other (same shape, different size). Similar shapes are linked by a scale factor.

40 min Video by Maths Genie AQA GCSE Maths

Similar ShapesWatch the walkthrough, then read the notes below.

Open on YouTube

What you'll learn

Tell congruent and similar shapes apart
Find a scale factor between similar shapes
Find missing lengths in similar shapes
Know the conditions for congruent triangles

Similar shapes

Similar shapes have equal angles and sides in the same ratio. Find the $scale factor$ by dividing a length on the big shape by the matching length on the small shape, then use it to find missing lengths.

1Scale factor

= 12 \div 4

= 3

AnswerScale factor 3

Congruent triangles

Triangles are congruent if they match by one of these conditions: $SSS$ (three sides), $SAS$ (two sides + included angle), $ASA$ (two angles + a side), or $RHS$ (right angle, hypotenuse, side).

Tip — Congruent = identical (scale factor 1). Similar = same shape, scaled.

Remember these

scale factor = \frac{big length}{small length}

For similar shapes.

SSS, SAS, ASA, RHS

Conditions for congruent triangles.

Watch out for these

Calling shapes congruent when one is an enlargement.

Congruent means identical; enlargements are only similar.

Dividing the wrong way for the scale factor.

Big ÷ small to enlarge; small ÷ big to reduce.

Key takeaways

Congruent = identical; similar = same shape, scaled.
Scale factor = matching big length ÷ small length.
Congruent triangles: SSS, SAS, ASA or RHS.

Test yourself

Ready to practise Similarity & Congruence? Pick a mode and earn XP & Dobloons.