Similar Triangles Calculator

Similar triangles have the same shape even when their sizes differ. Their corresponding angles are equal, and every pair of corresponding side lengths shares one constant ratio. That ratio is the scale factor. If Triangle 2 is twice as large as Triangle 1, each side in Triangle 2 is twice its matching side in Triangle 1, while every angle remains unchanged. The calculator labels two corresponding side pairs A1 with A2 and B1 with B2. Their central proportion is A1 / A2 = B1 / B2. Knowing any three positive lengths lets you solve the fourth by cross multiplication. To find A2, multiply A1 by B2 and divide by B1. To find B2, multiply B1 by A2 and divide by A1. The reverse formulas recover A1 or B1 in the same way. Correct correspondence matters more than the letters themselves. Match sides opposite equal angles before entering values. A side from Triangle 1 cannot be paired with an arbitrary side from Triangle 2. If the pairs are mismatched, the arithmetic may still produce a number, but that number will not describe the intended geometry. Drawing matching marks or writing vertices in corresponding order helps prevent this common error. Triangles can be proven similar through Angle-Angle when two angle pairs match, Side-Angle-Side when two side pairs are proportional around equal included angles, or Side-Side-Side when all three corresponding side ratios match. This calculator assumes similarity has already been established; it solves a missing side from the supplied proportion rather than proving that the original triangles are similar. Similar triangles support indirect measurement and scaling throughout everyday work. Surveyors can estimate an inaccessible height from shadows, mapmakers convert between drawing and ground distances, architects use scale models, and optics relates object and image dimensions. The scale factor returned here measures Triangle 2 relative to Triangle 1. A factor above one means Triangle 2 is larger, a factor below one means it is smaller, and a factor of one means the triangles are congruent as well as similar. All lengths must use the same unit or compatible converted units for the result to be meaningful.