Question

are the following similar? why or why not?
(image of two trapezoids: one with top base 4 in, bottom base 6 in; the other with top base 2 in, bottom base 6 in)
options:
no, the ratios of the corresponding sides are not equal.
no, the corresponding angles are not equal.
yes

Explanation:

Step1: Identify corresponding sides

For similar figures, corresponding sides must be in proportion. Let's take the two trapezoids. The first trapezoid has a top base of \(4\) in and the second has a top base of \(2\) in. The non - parallel side (or the other corresponding side) for both is \(6\) in.

Step2: Calculate the ratios

Calculate the ratio of the first pair of corresponding sides: \(\frac{4}{2}=2\). Calculate the ratio of the second pair of corresponding sides: \(\frac{6}{6} = 1\).

Step3: Compare the ratios

Since \(2
eq1\), the ratios of the corresponding sides are not equal. For two figures to be similar, the ratios of all corresponding sides must be equal (and corresponding angles must be equal, but in the case of trapezoids, if we consider the basic similarity condition for polygons, the side - length ratio condition is a key one here). So the trapezoids are not similar because the ratios of corresponding sides are not equal.

Answer:

No, the ratios of the corresponding sides are not equal.