# Similar Triangles Calculator

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?

## What are similar triangles?

Two triangles are * similar* if their

**corresponding sides**are in the

**same ratio**, which means that one triangle is a

**scaled**version of the other. Naturally, the

**corresponding angles**of similar triangles are

**equal**. For example, consider the following two triangles:

Notice that the corresponding sides are in proportion:

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

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

## Finding similar triangles: Law of similar triangles

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:

**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.

We can express this using a similar triangle formula:

where $k$ is the **scale factor**.

**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.

The triangles in the image above are similar if:

This rule is handy in cases like in the image below, where the triangles share an angle:

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

**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.

The triangles in the image above are similar if:

You can find the **third angle** if you know any two angles in a triangle using our triangle angle calculator. We know that if any two corresponding angles in the triangles are equal, the triangles are similar, meaning that in the **ASA congruence rule**, we don't need to know the side so long as the angles are known. However, without the sides, we cannot determine the **scale factor** $k$.

💡 Need to find the area of a triangle? We have our triangle area calculator that can help you with that.

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

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

**Find**the**scale factor**of the similar triangles by taking the`k`

**ratio**of any**known**side on the larger triangle and its corresponding side on the smaller one.**Determine**whether the triangle with the missing side is**smaller**or**larger**.- 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**.

For example, consider the following two similar triangles.

To find the missing side, we first start by calculating their **scale factor**.

Next, we use the scale factor relation between the **missing side AC** and its **corresponding side DF**:

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

## How do you find the area of a similar triangle?

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

**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.**Determine**whether the triangle with the unknown area is**smaller**or**larger**.- If the triangle is smaller,
**divide***A2*by the square of the**scale factor***k*to get*A1 = A2/k*. Otherwise,^{2}**multiply***A2*by*k*to get^{2}*A1 = A2 × k*.^{2}

## How to use this similar triangles calculator

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:

**Select**in the field**check similarity**`Type`

.**Choose**the similarity criterion you want to use. You can choose between**Side-Side-Side, Side-Angle-Side**, and**Angle-Side-Angle**.**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:

**Select**in the field**find the missing side**`Type`

.**Enter**the known dimensions, area, perimeter, and scale factor of the triangles. The similar triangles calculator will find the unknown values.

## FAQ

### Are all equilateral triangles similar?

**Yes**, if the corresponding angles of two triangles are equal, the triangles are similar. Since every angle in an equilateral triangle is equal to `60°`

, all equilateral triangles are similar.

### Find the scale factor of similar triangles whose areas are 10 cm² and 20 cm²?

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

**Divide**the larger area by the smaller area to get`20/10 = 2`

.**Find**the square root of this value to get the**scale factor**,`k = √2 = 1.414`

.- Verify this result using Omni's similar triangles calculator.