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Check whether two triangles are similar or find the missing length of a triangle with the help of this similar triangles calculator.
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Our similar triangles calculator lets you quickly check if two triangles are similar and compute any missing side lengths based on proportionality.
Similar triangles are triangles with identical shapes but not necessarily the same size. They maintain the same angles and have sides in proportion. Unlike congruent triangles, which match in both shape and size, similar triangles are indicated with the symbol ‘~’.
For triangles △ABC and △DEF, similarity (△ABC ~ △DEF) requires:
| Similar Triangles | Congruent Triangles |
|---|---|
| Same shape but different size | Same shape and same size |
| Symbol: ‘~’ | Symbol: ‘≅’ |
| Corresponding sides proportional | Corresponding sides equal |
Even without full knowledge of all sides and angles, these theorems help establish similarity:
If two angles of one triangle are equal to two angles of another, the triangles are similar.
If two sides are proportional and the included angle is equal, the triangles are similar.
If all three corresponding sides are proportional, the triangles are similar.
Check if △XYZ and △LMN are similar:
Calculating the third angles:
Since two pairs of angles are equal, △XYZ ~ △LMN by the AA theorem.
Enter known sides or angles, and the calculator can confirm similarity and solve for missing side lengths.
Output: Confirmation of similarity.
Output: Missing sides, areas, and perimeters of triangles.
No. Similar triangles share the same shape but differ in size; congruent triangles match in both shape and size.
Yes, all equilateral triangles are similar since all angles are equal.
For similar triangles with sides X, Y, Z and x, y, z: X:x = Y:y = Z:z
Right triangles with proportional corresponding sides are similar. Use the right triangle similarity calculator for accuracy.
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