Two triangles are similar if they have the same shape​ (but not necessarily the same​ size). Similar triangles have sides that are proportional.
Find the lengths x and y for the given pair of similar triangles.
10
26
32
8
y
x
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Part 1
xequals
  
enter your response here
yequals
  
enter your response here
 ​(Type integers or​ decimals.)

To solve for \( x \) and \( y \) in the pair of similar triangles, we use the property that corresponding sides of similar triangles are proportional. Let's set up the proportion equations.

Given the triangles, we know:

- For \( x \), we can set up a proportion based on corresponding sides:
\[
\frac{x}{32} = \frac{8}{26}
\]

- For \( y \), we set up a proportion for the corresponding sides as well:
\[
\frac{y}{10} = \frac{8}{26}
\]

### Solving for \( x \):
\[
x = \frac{8}{26} \times 32
\]
Now, let's calculate the value of \( x \).

### Solving for \( y \):
\[
y = \frac{8}{26} \times 10
\]
Now, I'll calculate both values.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you on how to solve this manually.

### Solving for \( x \):

\[
x = \frac{8}{26} \times 32
= \frac{256}{26} \approx 9.85
\]

So, \( x \approx 9.85 \).

### Solving for \( y \):

\[
y = \frac{8}{26} \times 10
= \frac{80}{26} \approx 3.08
\]

So, \( y \approx 3.08 \).

Let me know if you'd like further details or clarification.

### Related questions:
1. How do we know which sides are corresponding in similar triangles?
2. Can we find the angles if the triangles are similar?
3. What are other properties of similar triangles?
4. How do proportional sides help in finding unknown lengths in real-life applications?
5. Can we apply the same method for right triangles?

### Tip:
Always ensure that corresponding sides of the triangles are aligned properly before setting up proportions.

Two triangles are similar if they have the same shape​ (but not necessarily the same​ size). Similar triangles have sides that are proportional. Find the lengths x and y for the given pair of similar triangles. 10, 26, 32, 8, y, x.

Learn how to find the unknown side lengths x and y in a pair of similar triangles using proportions. This problem focuses on the geometric properties of similar triangles and the use of proportional relationships. Suitable for Grades 7-9 students.

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