Similar Triangles Calculator — Scale, Find Missing Side & Verify Similarity

What Are Similar Triangles?

Two triangles are similar if their corresponding sides are in the same ratio — meaning one triangle is a scaled version of the other. Because the side lengths are proportional, the corresponding angles are automatically equal.

We write △ABC ∼ △DEF to indicate similarity, where:

DE/AB = EF/BC = DF/AC = k  (scale factor)

The Law of Similar Triangles

Two triangles are similar if any one of these conditions holds:

• SSS (Side-Side-Side): All three pairs of corresponding sides are proportional.
• SAS (Side-Angle-Side): Two pairs of corresponding sides are proportional and the included angles are equal.
• AA (Angle-Angle): Two pairs of corresponding angles are equal (the third must be equal too, since angles sum to 180°).

How Do You Find the Missing Side of a Similar Triangle?

If △ABC ∼ △DEF with scale factor k, then every side of △DEF equals the corresponding side of △ABC multiplied by k:

DE = AB × k
EF = BC × k
DF = AC × k

To find a missing side, use a known corresponding pair to calculate k first, then multiply.

Example: If AB = 3, BC = 4, AC = 5 and DE = 6, EF = 8 (corresponding to AB and BC), then k = 6/3 = 2, and the missing side DF = 5 × 2 = 10.

How Do You Find the Area of a Similar Triangle?

The area of similar triangles scales by the square of the scale factor:

Area(△DEF) = Area(△ABC) × k²

If k = 2, the similar triangle has 4 times the area. If k = 0.5, it has ¼ the area. The perimeter scales linearly (by k), but the area scales quadratically (by k²).

How to Use This Similar Triangles Calculator

This calculator offers three modes:

1. Scale a Triangle: Enter all three sides (A, B, C) of the original triangle and a scale factor k. The calculator outputs the similar triangle's sides, both perimeters, and both areas.
2. Find Missing Side: Enter all three sides of Triangle 1 and two corresponding sides of Triangle 2. The calculator finds the missing third side using the proportionality rule.
3. Verify Similarity: Enter all six sides of both triangles. The calculator checks whether the triangles are truly similar (SSS rule) and shows the scale factor.

Choose Metric (mm, cm, m, km) or Imperial (in, ft, yd, mi) units to match your measurement system.

FAQs

What is the scale factor?

It is the ratio of any corresponding side of the larger triangle to the smaller one (k = larger ÷ smaller). If k > 1 the second triangle is bigger; if k < 1 it is smaller.

Can the scale factor be less than 1?

Yes. A scale factor of 0.5 means the second triangle has sides half as long and an area ¼ as large.

Do similar triangles have the same angles?

Always. If two triangles are similar, all three pairs of corresponding angles are equal, even if the side lengths differ.

What is the difference between similar and congruent triangles?

Congruent triangles have the same shape AND the same size (k = 1). Similar triangles have the same shape but may differ in size (k ≠ 1).

Which units does this calculator support?

Metric: mm, cm, m, km. Imperial: in (inches), ft (feet), yd (yards), mi (miles). Select your system before entering values.