Similar Triangles Calculator
Find a missing side using the scale factor between similar triangles.
Similar triangles have the same shape; corresponding sides are all in the same ratio.
How the Math Works
Similar triangles are triangles that have the same shape but different sizes, meaning all corresponding angles are equal and sides are proportional. The scale factor between similar triangles is found by dividing any side of the second triangle by its corresponding side in the first triangle (scale = a₂ ÷ a₁). Once this ratio is determined, it can be applied to find missing sides using the relationship b₂ = b₁ × scale. This works because the proportional relationships between all sides remain constant in similar triangles, allowing us to calculate unknown measurements when given partial information about two related triangles.
Practical Applications
To use this calculator, first identify corresponding sides between your two similar triangles. Measure or determine the length of one side in each triangle, then divide the side from the second triangle by its matching side in the first triangle to find the scale factor. Apply this factor to any known side from the first triangle by multiplying it by the scale factor to find the corresponding missing side in the second triangle. Always verify that your triangles are indeed similar by checking that all corresponding angles are equal before applying these calculations.
Day-to-Day Use
This calculation helps solve practical problems like measuring building heights using shadows, determining distances across obstacles like rivers or ravines, scaling blueprints for home projects, or calculating lens dimensions in photography equipment. Architects use it to scale models, surveyors apply it to measure inaccessible distances, and artists employ it when creating proportional drawings. Even everyday tasks like resizing photos, adjusting recipe quantities, or creating scale models for hobbies rely on these same proportional reasoning skills that similar triangles demonstrate.
Worked example
Sides 4 → 6 give scale 1.5, so a side of 5 becomes 7.5.
FAQ
Do angles change?
No — similar triangles have identical angles; only the sizes differ.