Things You Need to Know
- When we say that two shapes are "similar", we mean that their corresponding angles are equal and their corresponding sides are proportional.
- If the proportion for one pair of corresponding sides is different from another pair of corresponding sides, then the figure is not similar.
- To make a proportion, follow these steps:
- Identify the side you want to find the length of.
- Write a fraction with that unknown side in the numerator, and the length of its corresponding side in the denominator.
- Find another pair of corresponding sides, where with both sides the lengths are known.
- Write another fraction (set to be equal to your first fraction) with the known length of the side in the shape with the unknown side as the numerator, and the corresponding side as the denominator.
- Solve for the unknown side.
- Identify the side you want to find the length of.
- To determine if two shapes are similar, find the proportion of all the corresponding sides. If all the proportions are equal, then the shapes are similar.
- The value of the proportion between similar figures is known as the "scale factor". In other words, the scale factor is the number that you multiply each known side in one shape to get the length of the unknown side lengths in the other shape.
- To find the scale factor, write a fraction of the side length of the "new" shape over the side length of the "old" shape.
Interactive Activities
Sample Problems
Class Notes