What makes two triangles similar?
Two triangles are similar when their corresponding angles are equal and their corresponding sides are in the same ratio. They have the same shape but can be different sizes.
// maths › Foundations
Similar triangles & ratios
Find an unknown side of a triangle that is similar to another using the constant ratio between corresponding sides, with a visual that scales the two triangles together and shows the fixed scale factor.
a₁ / a₂ = b₁ / b₂ (corresponding sides are in proportion)
Frequently asked questions
What is the scale factor?
The scale factor is the constant ratio between corresponding sides. If one triangle's side of 3 matches another's side of 6, the scale factor is 6 ÷ 3 = 2, so every side of the second triangle is twice as long.
Can you show a worked example?
If side a₁ = 3 corresponds to a₂ = 6, the scale factor is 2. A side b₁ = 4 in the first triangle then matches b₂ = 4 × 2 = 8 in the second.
How does this connect to trigonometry?
Because similar right triangles share the same angles, their side ratios stay fixed. That constant ratio is exactly what sine, cosine, and tangent measure, so similarity is the foundation of trigonometry.
Where is this used in real life?
Architects and engineers use scale models and drawings, cartographers shrink real distances onto maps, photographers and film crews use similar-triangle optics for focus and framing, and surveyors find heights of tall objects from their shadows.