Congruence & Similarity

Compare shapes, identify consistent scale factors and distinguish similarity from exact congruence.

Curriculum rangeYears 7–11

Tap a pair of shapes to see whether they're congruent (same shape and size), similar (same shape, different size) or neither.

Congruent

Both shapes have sides 4 and 6 -- exactly the same size, so they're congruent (even though B may be rotated).

Learning notes

Congruence & Similarity essentials

Keep these rules beside you while you explore and practise.

Congruent shapes have exactly the same shape and size. Rotation, reflection or translation does not change congruence.

Corresponding angles are equal and all corresponding lengths share one scale factor.

k=\dfrac{\text{image length}}{\text{original length}}

\text{Length factor}=k\quad\text{Area factor}=k^2\quad\text{Volume factor}=k^3

Use SSS, SAS, ASA/AAS or RHS. AAA proves similarity only.

💡Match carefully: compare corresponding sides in the same order before calculating a scale factor.