Key Concepts: Congruent and Similar Solids

Congruent Solids

Two solids are congruent if they have exactly the same shape and size — all corresponding measurements are equal.

Similar Solids

Two solids are similar if they have the same shape and their corresponding measurements are proportional with scale factor k.

Ratios for Similar Solids (scale factor a : b)

• Corresponding lengths: a : b
• Surface areas: a² : b²
• Volumes: a³ : b³

Example

If two similar cylinders have radii in ratio 2 : 5, their volumes are in ratio 8 : 125.