BitWithBite
Geometry · Quick Reference
Similarity Cheat Sheet
In one line: similar figures have the same shape but not necessarily the same size — one is a scaled-up or scaled-down version of the other, with all angles matching and sides in the same proportion.
Key Ideas
1Similar Figures. Figures with the same shape: corresponding angles are equal, and corresponding sides are in proportion (the same ratio).
2Scale Factor. The ratio between corresponding side lengths of two similar figures, describing how much bigger or smaller one is than the other.
3AA Similarity (Angle-Angle). If two angles of one triangle equal two angles of another, the triangles are similar (the third angles must also match, since angles sum to 180°).
4Using Proportions to Find Missing Sides. Set up a ratio between corresponding sides of similar figures and solve for the unknown length.
5Similarity vs. Congruence. Congruent figures are always similar (scale factor of 1), but similar figures are only congruent if their scale factor equals 1.
Worked Examples
Triangle ABC has sides 3, 4, 5. Triangle DEF is similar with a scale factor of 2. Find the sides of DEF.
DEF has sides 6, 8, 10
Two similar triangles have corresponding sides 4 and 10. Find the scale factor.
Scale factor = 2.5
Two similar triangles have corresponding sides 6 and 9. If a side in the smaller triangle is 8, find the corresponding side in the larger triangle.
12
Formulas
Scale factor = (side of figure 2) / (corresponding side of figure 1)
Practice Yourself
Triangle ABC has sides 2,3,4. Triangle similar with scale factor 3. Find its sides.
6, 9, 12
Two similar triangles have corresponding sides 5 and 15. Find the scale factor.
3
What rule says two triangles are similar if two angles match?
AA similarity