Question

Determine whether the polygons to the right are similar. If​ so, write a similarity statement and give the scale factor. If​ not, explain.
Q
R
S
W
V
X
12
5
13
36
39
15
Question content area bottom
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
​Yes, Upper DeltaUpper VUpper WUpper X is similar to Upper DeltaUpper RUpper SUpper Q. The scale factor is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)
B.
​Yes, Upper DeltaUpper VUpper WUpper X is similar to Upper DeltaUpper QUpper RUpper S. The scale factor is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)
C.
​Yes, Upper DeltaUpper VUpper WUpper X is similar to Upper DeltaUpper SUpper QUpper R. The scale factor is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)
D.
​No, because the lengths of the corresponding sides are not proportional.
E.
​No, because the corresponding angles are not congruent.

Answer 1

To determine whether the polygons are similar, we need to check if the corresponding side lengths are in proportion.

Let's denote the side lengths of the first polygon (ΔVWX) as follows:
- VW = 12
- WX = 5
- XV = 13

And denote the side lengths of the second polygon (ΔQRS) as follows:
- QR = 36
- RS = 39
- SQ = 15

Now, we can find the ratios of the corresponding sides:
1. For side VW and QR:
\[
\frac{VW}{QR} = \frac{12}{36} = \frac{1}{3}
\]

2. For side WX and RS:
\[
\frac{WX}{RS} = \frac{5}{39}
\]

3. For side XV and SQ:
\[
\frac{XV}{SQ} = \frac{13}{15}
\]

Now we can analyze the ratios:

1. \(\frac{12}{36} = \frac{1}{3}\)

2. \(\frac{5}{39}\) does not simplify to \(\frac{1}{3}\).

3. \(\frac{13}{15}\) also does not simplify to \(\frac{1}{3}\).

Since the ratios of all corresponding sides are not equal, the polygons are not similar. Therefore, the correct conclusion is:

**D. No, because the lengths of the corresponding sides are not proportional.**