Similarity and Congruence

Congruence

Two shapes are congruent if all corresponding sides and angles are equal.

Triangle congruence: SSS, SAS, ASA, AAS, RHS.

Similarity

Two shapes are similar if one is an enlargement of the other. Corresponding angles are equal and corresponding sides are in the same ratio.

Scale Factors

If the length scale factor is $k$:

• Lengths scale by $k$
• Areas scale by $k^2$
• Volumes scale by $k^3$

Example

Two similar cones have height ratio 2:5. If the smaller has volume 24 cm³:

Volume ratio = $2^3 : 5^3 = 8 : 125$.

Larger volume = $24 \times \frac{125}{8} = 375$ cm³.