Similar Triangles Calculator

Enter the three sides of Triangle ABC (AB, BC, AC) and at least two sides of Triangle DEF to find the missing side using similar triangle ratios. You can also enter a scale factor directly to scale all sides of the first triangle. The calculator returns the scale factor, all sides of the second triangle, and a visual breakdown of the proportional relationship between the two triangles.

cm
cm
cm

Choose whether to enter a scale factor or a known side of Triangle DEF.

Enter the ratio by which Triangle ABC is scaled to get Triangle DEF.

cm

Corresponds to side AB. Leave blank if using scale factor.

cm

Corresponds to side BC. Optional — used to verify the scale factor.

cm

Corresponds to side AC. Optional — used to verify the scale factor.

Results

Scale Factor (k = DEF / ABC)

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Side DE

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Side EF

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Side DF

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Perimeter of △ABC

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Perimeter of △DEF

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Area of △ABC

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Area of △DEF

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Side Lengths: △ABC vs △DEF

Results Table

Frequently Asked Questions

What are similar triangles?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. This means one triangle is essentially a scaled version of the other — it can be larger, smaller, or the same size, but the shape remains identical.

How do you find the missing side of a similar triangle?

To find a missing side, set up a proportion using the known corresponding sides. If triangles ABC and DEF are similar, then AB/DE = BC/EF = AC/DF = k (the scale factor). Multiply any known side of △ABC by k to get the corresponding side of △DEF.

What is the scale factor of similar triangles?

The scale factor is the constant ratio between any pair of corresponding sides of two similar triangles. For example, if AB = 3 cm and DE = 6 cm, the scale factor k = DE/AB = 2. All other sides of △DEF will be exactly twice those of △ABC.

How do you find the area of a similar triangle?

The ratio of the areas of two similar triangles equals the square of the scale factor. So if k is the scale factor, then Area(DEF) / Area(ABC) = k². For example, if k = 2, the area of △DEF is 4 times the area of △ABC.

Are all equilateral triangles similar?

Yes — all equilateral triangles are similar to each other. Since every equilateral triangle has three 60° angles, the AA (Angle-Angle) similarity criterion is automatically satisfied for any two equilateral triangles, regardless of their side lengths.

Are similar triangles and congruent triangles the same?

No. Similar triangles have the same shape but can differ in size, meaning their sides are proportional with a scale factor that may or may not equal 1. Congruent triangles are a special case of similar triangles where the scale factor is exactly 1, meaning all corresponding sides and angles are equal.

What are the key theorems used to prove triangle similarity?

The three main similarity theorems are: AA (Angle-Angle) — two pairs of corresponding angles are equal; SSS (Side-Side-Side) — all three pairs of corresponding sides are proportional; and SAS (Side-Angle-Side) — two pairs of sides are proportional and the included angles are equal.

How do I calculate the side ratios of similar triangles?

Divide each side of one triangle by the corresponding side of the other triangle. For truly similar triangles, all three ratios (AB/DE, BC/EF, AC/DF) must be equal. This common ratio is the scale factor k. If the ratios differ, the triangles are not similar.

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