Missing Side in Similar Figures

Similar figures: key idea

Similar figures have the same shape, so matching sides are proportional. If one side in a figure is missing, you can find it by setting up a proportion with the corresponding side lengths from the other figure.

Method

1. Match the correct sides. Make sure each side you compare is in the same position on the two similar figures.
2. Write a proportion. Set one ratio of corresponding sides equal to another ratio.
3. Solve for the missing side. Multiply across and divide if needed.
4. Simplify the answer. If the result is a fraction or ratio that can be reduced, write it in simplest form.

Helpful check

After solving, compare the scale factor on both figures. The ratio between corresponding sides should be consistent. If your answer makes the two figures no longer proportional, recheck the side matches and arithmetic.

Example strategy

If one figure has a known side of 6 and the matching side on the other figure is 9, then the scale factor is 9/6 = 3/2. Use that same factor on every other pair of corresponding sides to find the missing length.

Common mistake to avoid

Do not compare nonmatching sides. The left side must match the left side, the top with the top, and so on, according to the figures’ layout.