Similar Triangles Calculator (2024)

This similar triangles calculator is here to help you find a similar triangle by scaling a known triangle. You can also use this calculator to find the missing length of a similar triangle!

Stick around and scroll through this article as we discuss the laws of similar triangles and learn some fundamentals:

• What are similar triangles?
• Finding similar triangles: How do you determine whether two triangles are similar?
• How do you find the missing side of a similar triangle?
• How do you find the area of a similar triangle?

Therefore, we can say $\triangle \text{ABC}$△ABC $\sim$∼ $\triangle \text{DEF}$△DEF. Here the symbol $\sim$∼ indicates that the triangles are similar.

We term the proportion of similarity as the scale factor $(k)$(k). In the example above, the scale factor $k = 2$k=2. If you need help finding ratios, use our ratio calculator.

We know that two triangles are similar if either of the following is true:

• The corresponding sides of the triangle are in proportion; or
• The corresponding angles are equal.

From this, we can derive specific rules to determine whether any two triangles are similar:

1. Side-Side-Side (SSS): If all three corresponding sides of the two triangles are in proportion, they are similar. This rule is the most straightforward and requires you to know all the sides of the triangles.

where $k$k is the scale factor.

2. Side-Angle-Side (SAS): If any two corresponding sides of two triangles are in proportion and their included angles are equal, then the triangles are similar. We can use this rule whenever we know only two sides of each triangle and their included angles.

You can do many things knowing just the Side-Angle-Side of a triangle. Learn more using our SAS triangle calculator.

3. Angle-Side-Angle (ASA): If any two corresponding angles of two triangles are equal and the corresponding sides between them are in proportion, the triangles are similar.

To find the missing side of a triangle using the corresponding side of a similar triangle, follow these steps:

1. Find the scale factor k of the similar triangles by taking the ratio of any known side on the larger triangle and its corresponding side on the smaller one.
2. Determine whether the triangle with the missing side is smaller or larger.
3. If the triangle is smaller, divide its corresponding side in the larger triangle by k to get the missing side. Otherwise, multiply the corresponding side in the smaller triangle by k to find the missing side.

🙋 You can also compare two right triangles and see their similarities using our Check Similarity in Right Triangles Calculator.

To find the area of a triangle A1 from the area of its similar triangle A2, follow these steps:

1. Find the scale factor k of the similar triangles by taking the ratio of any known side on the larger triangle and its corresponding side on the smaller one.
2. Determine whether the triangle with the unknown area is smaller or larger.
3. If the triangle is smaller, divide A2 by the square of the scale factor k to get A1 = A2/k². Otherwise, multiply A2 by k² to get A1 = A2 × k².

Now that you've learned how to find the length of a similar triangle, the similar triangles formula, and more, you can quickly figure out how this similar triangles calculator works.

To check whether two known triangles are similar, use this calculator as follows:

1. Select check similarity in the field Type.
2. Choose the similarity criterion you want to use. You can choose between Side-Side-Side, Side-Angle-Side, and Angle-Side-Angle.
3. Enter the dimensions of the two triangles. The calculator will evaluate whether they are similar or not.

To use this calculator to solve for the side or perimeter of similar triangles, follow these steps:

1. Select find the missing side in the field Type.
2. Enter the known dimensions, area, perimeter, and scale factor of the triangles. The similar triangles calculator will find the unknown values.

1.414. To determine this scale factor based on the two areas, follow these steps:

1. Divide the larger area by the smaller area to get 20/10 = 2.
2. Find the square root of this value to get the scale factor, k = √2 = 1.414.
3. Verify this result using Omni's similar triangles calculator.