If you know two figures are similar, how can you find the missing lengths for the second figure?. Sample problem here.

Definition: Similar figures are figures that are the exact same shape, but are different sizes. Similar figures Not similar figures Two figures are similar if the lengths of their corresponding sides form a proportion.

Example 1

These two triangles are similar. We can prove that they are similar using a ratio table to compare the lengths of their corresponding sides.

• In the table, you can see that the ratio of the bases is 15/20. This reduces to $\frac{3}{4}$.
• Also in the table you can see that the ratio of the two right sides is 6/8. This reduces to $\frac{3}{4}$.
• Finally, the ratio of the two left sides is 12/16. This reduces to $\frac{3}{4}$.

Since all three ratios are equivalent, then the two triangles are similar.

Directions:

1. Use the "shapeswitcher" to choose the similar figures.
2. Move the vertices, sides, and figures themselves.
3. Notice that the lengths change, but the two figures maintain their similarity.
4. Use the "Show/Hide ratios" button to verify that the ratios are indeed equivalent.

Example 2

These two triangles are similar. Find the missing length.

To find the missing length we need to create a ratio table, like so... 

Once the table is made, it is up to you to figure out this missing value. In this case, the missing value is 15 cm. Can you see how to get that answer?

Need a hint? [show the hint]

Directions:

1. Move the vertices of the similar triangles.
2. Use proportions to find the missing lengths.
3. Pull down the sliders to check your answers.

Self-Check