If two parallelograms are similar, what do you know about the
ratios of the two side lengths within one parallelogram and the
ratios of the corresponding side lengths in the other
parallelogram?
Equal, if we are comparing the corresponding sides.
If two parallelograms are similar, it means that their corresponding angles are equal, and the ratio of their corresponding side lengths is the same. In other words, the sides of the two parallelograms are proportional to each other.
To understand the ratios of the side lengths within and between the parallelograms, you can follow these steps:
1. Identify the corresponding sides: Identify the sides in one parallelogram that are in the same position as the sides in the other parallelogram. For example, the top side of one parallelogram corresponds to the top side of the other parallelogram.
2. Measure the side lengths: Measure the lengths of the corresponding sides in both parallelograms.
3. Compare the ratios: Divide the length of one side in one parallelogram by the length of the corresponding side in the other parallelogram. Repeat this for all corresponding sides.
4. Analyze the ratios: If the ratios for all corresponding sides are equal, it indicates that the two parallelograms are similar. This means that the lengths of the sides are proportional to each other.
For example, if the ratio of the lengths of the corresponding sides in one parallelogram is 2:1, then the ratio of the corresponding sides in the other parallelogram will also be 2:1.
Remember, the ratios of the side lengths within one parallelogram will be the same as the ratios of the corresponding side lengths in the other parallelogram if they are similar.