Question

Determine whether the polygons to the right are similar. If​ so, write a similarity statement and give the scale factor. If​ not, explain.
A
B
C
J
H
K
15
8
17
45
51
24
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 HUpper JUpper K is similar to Upper DeltaUpper AUpper BUpper C. The scale factor is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)
B.
​Yes, Upper DeltaUpper HUpper JUpper K is similar to Upper DeltaUpper CUpper AUpper B. The scale factor is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)
C.
​Yes, Upper DeltaUpper HUpper JUpper K is similar to Upper DeltaUpper BUpper CUpper A. 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 if the polygons (triangles) ΔHJK and ΔABC are similar, we need to check if the corresponding sides are proportional and if the corresponding angles are congruent.

Given the side lengths:
- For ΔHJK: 15, 8, 17
- For ΔABC: 45, 51, 24

We will compare the fractions of the corresponding sides:

1. Compare 15 and 45:
\[
\frac{15}{45} = \frac{1}{3}
\]

2. Compare 8 and 24:
\[
\frac{8}{24} = \frac{1}{3}
\]

3. Compare 17 and 51:
\[
\frac{17}{51} = \frac{1}{3}
\]

Since all three pairs of corresponding sides have the same ratio \( \frac{1}{3} \), the triangles are similar.

Thus, we can say:

**Answer:**
A. Yes, ΔHJK is similar to ΔABC. The scale factor is \( \frac{1}{3} \).