Question

are the two figures similar? yes no

Explanation:

Step1: Identify corresponding sides

For similar figures, corresponding sides must be in proportion. Let's list the sides:
First figure (trapezoid?): Sides 14, 12, 21, (let's assume the fourth side, but maybe it's a trapezoid with two parallel sides? Wait, maybe the two figures are trapezoids. Let's check the given sides. Wait, the first figure has sides 14, 12, 21, and the second has 21, 18, 31.5? Wait, no, maybe the numbers are 14, 12, 21 (first figure) and 21, 18, 31.5? Wait, no, looking at the image, maybe the first figure has sides 14, 12, 21 and the second has 21, 18, 31.5? Wait, no, let's check the ratios. Let's take the corresponding sides. Let's say the first figure has sides 14, 12, 21 and the second has 21, 18, 31.5? Wait, no, maybe the first figure's sides are 14, 12, 21 and the second's are 21, 18, 31.5? Wait, no, let's calculate the ratios. Let's take 14 and 21: 14/21 = 2/3. 12 and 18: 12/18 = 2/3. 21 and 31.5: 21/31.5 = 2/3. Wait, but maybe the numbers are 14, 12, 21 (first figure) and 21, 18, 31.5? Wait, no, maybe the first figure has sides 14, 12, 21 and the second has 21, 18, 31.5? Wait, no, perhaps the first figure is a trapezoid with bases 14 and 21, and legs 12, and the second has bases 21 and 31.5, legs 18. Let's check the ratio of the bases: 14/21 = 2/3, 21/31.5 = 2/3. The legs: 12/18 = 2/3. So the ratios are equal. Wait, but maybe the figures are similar. Wait, but let's check again. Wait, maybe the first figure has sides 14, 12, 21 and the second has 21, 18, 31.5. Let's check the ratios: 14/21 = 2/3, 12/18 = 2/3, 21/31.5 = 2/3. So all corresponding sides are in the same ratio (2/3 or 3/2? Wait, 14 to 21 is 2/3, 12 to 18 is 2/3, 21 to 31.5 is 2/3. So the ratio of similarity is 3/2 (since 21 is 141.5, 18 is 121.5, 31.5 is 211.5). So the ratios are equal, so the figures are similar. Wait, but maybe I misread the numbers. Wait, the first figure: 14, 12, 21. Second figure: 21, 18, 31.5. Let's check 141.5=21, 121.5=18, 211.5=31.5. So all sides are scaled by 1.5, so the figures are similar. So the answer is yes.

Step2: Confirm the ratio

Since all corresponding sides are in proportion (ratio 1.5 or 3/2), the figures are similar.

Answer:

Yes