Determine whether the polygons to the right are similar. If so, write a similarity statement and give the scale factor If not, explain. Select the correct choice and fill in any answer boxes in your choice below. Yes, $$ \Delta H J K \sim \Delta \mathrm{VWX} $$. The scale factor of $$ \Delta H J K $$ to $$ \Delta \mathrm{VWX} $$ is B. No, because lengths of corresponding sides are not proportional. (Type an integer or a simplified fraction.) C. Yes, $$ \Delta H J K \sim \Delta X V W $$. The scale factor of $$ \Delta H J K $$ to $$ \Delta X \mathrm{VW} $$ is $$ \square $$. (Type an integer or a simplified fraction.) D. Yes, $$ \Delta H J K \sim \Delta V X W $$. The scale factor of $$ \Delta H J K $$ to $$ \Delta \mathrm{VXW} $$ is $$ \square $$. (Type an integer or a simplified fraction.) Ho, because corresponding angles are not congruent. Help me solve this View an example Get more help a

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UpStudy AI · Accepted Answer

To determine whether the polygons $$ \Delta HJK $$ and $$ \Delta VWX $$ are similar, we need to check two main conditions:

1. **Corresponding Angles**: The angles of the two triangles must be congruent.
2. **Proportional Sides**: The lengths of the corresponding sides must be proportional.

### Step 1: Check Corresponding Angles
If we have the measures of the angles of both triangles, we can compare them. If all corresponding angles are equal, we can proceed to check the sides.

### Step 2: Check Proportional Sides
To check if the sides are proportional, we can use the following formula for the scale factor $$ k $$:

$$
k = \frac{\text{length of side in } \Delta HJK}{\text{length of corresponding side in } \Delta VWX}
$$

We need to calculate the ratios of all corresponding sides and see if they are equal.

### Conclusion
- If both conditions are satisfied, we can conclude that the triangles are similar, and we can write a similarity statement such as $$ \Delta HJK \sim \Delta VWX $$ and provide the scale factor.
- If either condition fails, we will conclude that the triangles are not similar and provide the reason.

### Example Calculation
Assuming we have the following side lengths:
- $$ HJ = a $$, $$ JK = b $$, $$ KH = c $$
- $$ VW = d $$, $$ WX = e $$, $$ XV = f $$

We would calculate:
$$
\text{Scale factor for } HJ \text{ to } VW = \frac{a}{d}
$$
$$
\text{Scale factor for } JK \text{ to } WX = \frac{b}{e}
$$
$$
\text{Scale factor for } KH \text{ to } XV = \frac{c}{f}
$$

If all three ratios are equal, then the triangles are similar.

### Final Decision
Please provide the measures of the angles and the lengths of the sides for both triangles $$ \Delta HJK $$ and $$ \Delta VWX $$ so that we can perform the calculations and reach a conclusion.
The triangles $$ \Delta HJK $$ and $$ \Delta VWX $$ are not similar because the lengths of their corresponding sides are not proportional.

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