the corresponding sides of similar polygons are ?
... in the same proportion, for any pair of corresponding sides.
The corresponding sides of similar polygons are the sides that are in the same relative position to each other in each polygon. This means that the corresponding sides have the same ratio of lengths.
To determine the corresponding sides of similar polygons, you can follow these steps:
1. Identify the polygons: Determine which polygons are similar to each other. Similar polygons have the same shape but possibly different sizes.
2. Compare the corresponding angles: Check if the corresponding angles in both polygons are equal. If the angles are equal, it is an indication that the polygons are similar.
3. Compare the side lengths: Once you have established that the polygons are similar based on their angles, you can compare the side lengths. Corresponding sides are the sides that have the same relative position in each polygon.
4. Determine the ratio: Calculate the ratio of the lengths of the corresponding sides by dividing the length of one side in one polygon by the length of the corresponding side in the other polygon.
For example, if you have two similar triangles, ABC and DEF, and you know that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F, you can compare the side lengths of the triangles. If side AB is 4 units long and side DE is 8 units long, then the ratio of AB to DE is 4:8, or 1:2. This ratio applies to all the corresponding sides of the triangles.
Remember that the corresponding sides of similar polygons have the same ratio. This property can be useful in solving problems involving similar polygons, such as finding missing side lengths or scale factors.