How to Find an Unknown Side of Similar Triangles

Repositioning similar triangles can help you identify corresponding sides.

Although two similar shapes may be different sizes, they have the same form. All of the corresponding angles in two similar triangles have the same measure and their corresponding sides are proportional. This proportionality means that if you know the lengths of two sides in one triangle and one in the other, you can find the missing side in the second triangle. Viewing the problem algebraically lets you represent the side with a variable such as "X."

Instructions

1. Draw both triangles so that they face the same way and so that their corresponding angles are in the same positions. Label all three known sides.

2. Write a fraction by placing the number representing the length of one side of one triangle over the length of the side in the same position on the other triangle.

3. Write another fraction using the single known side and an "X" for the missing side. If the "X" is from the same triangle as the top number in the other fraction, put it in the top of the second fraction. If it is from the same triangle as the bottom number in the first fraction, put it in the bottom.

4. Set the two fractions equal to each other and cross multiply to make an algebraic equation. For instance, if you had 4/5 = x/10, you would get 40=5x.

5. Solve the equation for "X" to find the answer for the missing side. For instance, in the case of 40 = 5x, you would divide both sides by 5 and get x = 8.

References

• Purple Math: Solving Proportions