Question

are the polygons below similar?
h 4
10
g j
u 15
t
25
r
s
yes
no

Explanation:

Step1: Recall similarity of rectangles

For rectangles to be similar, their corresponding sides must be in proportion. Let's denote the first rectangle (H, G, J, H?) with length 10 and width 4, and the second rectangle (U, T, S, R) with length 25 and width 15.

Step2: Check the ratios of corresponding sides

Calculate the ratio of the lengths: $\frac{10}{25}=\frac{2}{5}$. Calculate the ratio of the widths: $\frac{4}{15}$. Since $\frac{2}{5}
eq\frac{4}{15}$, the sides are not in proportion. Wait, wait, maybe I mixed up length and width. Wait, first rectangle: sides 10 and 4; second rectangle: sides 25 and 15. Let's check $\frac{10}{15}=\frac{2}{3}$ and $\frac{4}{25}$? No, wait, maybe the first rectangle's length is 10, width 4; second rectangle's length is 25, width 15. Wait, no, maybe the first rectangle: height 10, width 4; second rectangle: height 25, width 15. So ratio of heights: 10/25 = 2/5; ratio of widths: 4/15. Wait, that's not equal. Wait, maybe I got the sides wrong. Wait, the first rectangle: horizontal side 4, vertical side 10. The second rectangle: horizontal side 15, vertical side 25. So ratio of horizontal sides: 4/15, ratio of vertical sides: 10/25 = 2/5. 4/15 ≈ 0.2667, 2/5 = 0.4. Not equal. Wait, but wait, maybe the rectangles are rotated? Wait, no, similarity doesn't depend on rotation, but on proportional sides. Wait, maybe I made a mistake. Wait, 10 and 25: 10/25 = 2/5; 4 and 15: 4/15. No, that's not equal. Wait, but wait, maybe the first rectangle is 4 (width) and 10 (height), second is 15 (width) and 25 (height). So 4/15 vs 10/25. 10/25 is 2/5, 4/15 is less. Wait, but maybe the other way: 10/15 and 4/25? No. Wait, maybe the problem is that I misassigned the sides. Wait, the first rectangle: two sides 10 and 4, all angles 90 degrees. The second rectangle: two sides 25 and 15, all angles 90 degrees. For similarity, the ratios of corresponding sides must be equal. So 10/25 = 2/5, 4/15 ≈ 0.2667. 2/5 is 0.4, not equal. Wait, but wait, maybe I flipped the sides. Let's check 10/15 and 4/25. 10/15 = 2/3, 4/25 = 0.16. No. Wait, this is confusing. Wait, maybe the correct ratios are 10/25 = 2/5 and 4/15? No, that's not equal. Wait, but maybe the first rectangle is 4 (length) and 10 (width), second is 15 (length) and 25 (width). Then 4/15 and 10/25. 10/25 is 2/5, 4/15 is 4/15. 2/5 is 6/15, which is not equal to 4/15. So the ratios are not equal. Therefore, the rectangles are not similar. Wait, but the answer options are yes or no. Wait, maybe I made a mistake. Wait, 10 and 25: 102.5=25; 42.5=10, but 42.5=10, but 15 is not 10. Wait, no, 43.75=15, 103.75=37.5, not 25. Wait, 102.5=25, 4*2.5=10, but the second rectangle's other side is 15, not 10. So the sides are 10,4 and 25,15. So 10/25=2/5, 4/15. Not equal. So the answer is no.

Answer:

no