What are similar triangles?

Similar triangles are triangles with the same shape. Their angles are equal in pairs, and their corresponding side lengths have the same ratio. They may be different sizes, but one is a scaled version of the other.

How do you find a missing side in similar triangles?

Set up a proportion using corresponding sides. If a side in the first triangle corresponds to a side in the second triangle, their ratio must match the ratio of another corresponding pair. Then solve the proportion for the missing side.

What does scale factor mean?

The scale factor tells how many times larger or smaller one triangle is compared with the other. If the scale factor from triangle 1 to triangle 2 is 2, every side in triangle 2 is twice the corresponding side in triangle 1.

Can triangles be similar if they are rotated or flipped?

Yes. Rotation, reflection, and position do not matter. Similarity depends on angle equality and proportional side lengths, not on how the triangles are drawn on the page.

Education

Similar Triangles Calculator

Solve similar-triangle proportions, find missing corresponding sides, check side-ratio similarity, and calculate scale factor with steps. This page is written for students who need both a fast answer and a clear explanation of the method, so it includes the formula, steps, examples, common mistakes, and practical notes.

How similar triangles work

Similar triangles have the same shape but not necessarily the same size. Their corresponding angles match, and their corresponding side lengths are proportional. The OpenStax triangle similarity and triangle properties lesson explains this proportional-side relationship, which is the main idea behind this calculator.

Formula and example

Corresponding side ratio: a₁ / a₂ = b₁ / b₂ Missing side form: x = a₂ × b₁ ÷ a₁ Example: 3 corresponds to 6, and 5 corresponds to x x = 6 × 5 ÷ 3 = 10

The hardest part is usually not the arithmetic. It is matching the correct corresponding sides. Always compare the sides that face equal angles.

Common questions

Similar triangles are triangles with the same shape. Their angles are equal in pairs, and their corresponding side lengths have the same ratio. They may be different sizes, but one is a scaled version of the other.
Set up a proportion using corresponding sides. If a side in the first triangle corresponds to a side in the second triangle, their ratio must match the ratio of another corresponding pair. Then solve the proportion for the missing side.
The scale factor tells how many times larger or smaller one triangle is compared with the other. If the scale factor from triangle 1 to triangle 2 is 2, every side in triangle 2 is twice the corresponding side in triangle 1.
Yes. Rotation, reflection, and position do not matter. Similarity depends on angle equality and proportional side lengths, not on how the triangles are drawn on the page.