Similar Triangles Calculator

Find unknown sides of similar triangles using proportional relationships.

Enter Known Sides

Triangle 1 (ABC)
Triangle 2 (DEF) — similar to Triangle 1

Result

Scale Factor
2
ratio
Triangle 1: a3
Triangle 1: b4
Triangle 1: c5
Triangle 2: d6
Triangle 2: e8
Triangle 2: f10

Step-by-Step Solution

a/d = b/e = c/f (proportional sides)

Understanding Similar Triangles

Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. This means one triangle is a scaled version of the other. The ratio between corresponding sides is called the scale factor.

Key Properties

AA (Angle-Angle) Similarity

If two angles of one triangle equal two angles of another, the triangles are similar.

If angle A = angle D and angle B = angle E, then ABC ~ DEF

SSS (Side-Side-Side) Similarity

If all three pairs of corresponding sides are proportional, the triangles are similar.

a/d = b/e = c/f

SAS (Side-Angle-Side) Similarity

If two pairs of sides are proportional and the included angles are equal.

a/d = b/e and angle A = angle D

How to Solve

  1. Identify which sides correspond between the two triangles.
  2. Find the scale factor using a pair of known corresponding sides.
  3. Multiply or divide by the scale factor to find unknown sides.

Practical Applications

Similar triangles are used in surveying to measure inaccessible distances, in photography for perspective calculations, in engineering for scale models, and in trigonometry for deriving relationships between angles and sides.