Similar Triangle Side Length Calculator

Discover the missing side of a triangle similar to another. Enter the known side lengths and let's calculate!

Enter Side Lengths

Provide the known side lengths for Triangle 1 and Triangle 2 to calculate the unknown side.

Triangle 1

Side 1:

Side 2:

Triangle 2

Side 1 (Corresponding):

Side 2 (Unknown):

Calculated Side Length (Triangle 2, Side 2):

Visualization of Similar Triangles

Note: Triangles are not to scale but represent the concept of similarity.

Understanding Similar Triangles

Similar triangles are triangles that have the same shape, but can be different sizes. This means their corresponding angles are equal, and their corresponding sides are in proportion.

Key Properties of Similar Triangles:

Corresponding Angles are Equal: If two triangles are similar, then the angles in the same positions in each triangle are equal.
Corresponding Sides are Proportional: The ratios of the lengths of corresponding sides are equal. This is the principle our calculator uses.

Formula for Side Length Calculation:

For two similar triangles, if we know two sides of the first triangle (Side 1₁, Side 2₁) and one corresponding side of the second triangle (Side 1₂), we can find the other corresponding side (Side 2₂) using the proportion:

$$ \frac{\text{Side 2}_{\text{Triangle 2}}}{\text{Side 2}_{\text{Triangle 1}}} = \frac{\text{Side 1}_{\text{Triangle 2}}}{\text{Side 1}_{\text{Triangle 1}}} $$

Rearranging this formula to solve for the unknown Side 2 of Triangle 2:

$$ \text{Side 2}_{\text{Triangle 2}} = \frac{{\text{Side 2}_{\text{Triangle 1}} \times \text{Side 1}_{\text{Triangle 2}}}}{\text{Side 1}_{\text{Triangle 1}}} $$

Use this calculator to quickly find the length of a side in a similar triangle, making geometry problems easier and faster to solve!