Similar Shapes and Scale Factors
Grade 5What makes shapes similar?
Two shapes are similar if they have the same shape but different sizes — all corresponding angles are equal and all corresponding sides are in the same ratio. That ratio is the scale factor.
Similar shapes are like enlargements of each other. Congruent shapes are a special case where the scale factor is 1.
Finding missing lengths
Find the scale factor by dividing a known side of the larger shape by the corresponding side of the smaller shape. Then multiply (or divide) the other sides by the same factor.
Always match corresponding sides — sides opposite equal angles. Writing the sides in a ratio table helps: small shape on top, large on bottom, same position in each column.
Worked example
EXAMPLE
Two similar triangles have corresponding sides 4 cm and 10 cm. The smaller triangle has a second side of 6 cm. Find the corresponding side in the larger triangle.
Scale factor = 10 ÷ 4 = 2.5. Missing side = 6 × 2.5 = 15 cm.
