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?
The ratios would be the same in similar parallelograms.
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?
48
900
If these two shapes are similar, what is the measure of the missing length d?
=d5
s e x y
To understand why the ratios of the corresponding side lengths in similar parallelograms are the same, let's consider the definition of similarity. Two figures are considered similar when their corresponding angles are congruent and their corresponding side lengths are proportional.
In the case of parallelograms, we can observe that opposite sides of a parallelogram are equal in length. Therefore, if two parallelograms are similar, it means that the corresponding sides of these parallelograms are in proportion.
Let's denote the two parallelograms as Parallelogram A and Parallelogram B. If we take one side length of Parallelogram A and its corresponding side length of Parallelogram B, we can set up a proportion to compare them, like this:
(A side length of Parallelogram A) / (corresponding side length of Parallelogram A) = (A side length of Parallelogram B) / (corresponding side length of Parallelogram B)
Since similar figures have proportional sides, this equation holds true for all corresponding side lengths within the parallelograms.
Therefore, in conclusion, when two parallelograms are similar, the ratios of the side lengths within one parallelogram are equal to the ratios of the corresponding side lengths in the other parallelogram.