Similar shapes: how to solve
When two shapes are similar, their corresponding angles are equal and their corresponding side lengths are in the same ratio. The key idea is to match the correct sides before doing any calculation.
1) Identify corresponding parts
- Match corners with equal angles.
- Write down which sides belong together.
- Keep the order consistent so the ratio is the same on both shapes.
2) Find the scale factor
- Compare one known side on the first shape with its matching side on the second shape.
- Write a ratio or scale factor.
- If the answer asks for a missing side, set up a proportion using matching sides.
3) Solve for the unknown
- Multiply or divide by the scale factor as needed.
- Keep the fraction or ratio exact if possible.
- Simplify the final answer fully.
4) Check your work
- Compare the side lengths again to make sure all corresponding sides have the same ratio.
- Check that any angle information is still consistent.
- If your result is a length, it should fit the size change between the shapes.
A good habit is to label the matching sides directly on the diagram before calculating. That makes it much easier to avoid mixing up the ratios.