https://file.aiquickdraw.com/mathbot/file/1725497542933s826zynb.jpg

State if the triangles are similar. If so, state the postulate and the similarity statement

To determine if the triangles in the image are similar, we'll analyze their corresponding angles and sides.

### Step 1: Identify the Triangles and Corresponding Parts
The two triangles in the image are:
1. Triangle \(UVW\)
2. Triangle \(GFH\)

### Step 2: Compare Angles
- Both triangles have an angle of \(76^\circ\).
- Since both triangles share this angle, and each triangle is a right triangle (as the other angles are \(90^\circ\)), the triangles have two pairs of corresponding angles that are equal.

### Step 3: Compare Sides
For the triangles to be similar by the Angle-Angle (AA) postulate, we don’t necessarily need to compare sides. However, to verify similarity through the Side-Angle-Side (SAS) or Side-Side-Side (SSS) postulates, we would compare the corresponding sides.

For Triangle \(UVW\):
- \(UV = 18\)
- \(UW = 9\)

For Triangle \(GFH\):
- \(GH = 21\)
- \(GF = 42\)

### Step 4: Check for a Constant Ratio Between Corresponding Sides
We check if the corresponding sides are proportional:
- \( \frac{UV}{GH} = \frac{18}{21} = \frac{6}{7} \)
- \( \frac{UW}{GF} = \frac{9}{42} = \frac{3}{14} \)

These ratios are not equal, so the triangles are not similar by the SAS or SSS postulates. However, since the corresponding angles are equal, **the triangles are similar by the AA postulate**.

### Conclusion:
The triangles are **similar** by the **Angle-Angle (AA) postulate**. The similarity statement is:
\[
\triangle UVW \sim \triangle GFH
\]

Would you like more details, or do you have any questions about this?

Here are five related questions you might find interesting:
1. What other postulates can be used to determine triangle similarity?
2. How do we determine the proportionality of sides in similar triangles?
3. What happens if two triangles have three pairs of corresponding sides that are proportional?
4. How can we use similar triangles to find missing side lengths?
5. Can two triangles with the same angles but different sizes be congruent?

**Tip:** When dealing with triangles, remember that the sum of all interior angles is always \(180^\circ\). This fact can help you quickly identify or confirm angles.

State if the triangles are similar. If so, state the postulate and the similarity statement.

Learn how to determine if two triangles are similar using the Angle-Angle (AA) postulate. In this problem, the triangles UVW and GFH are examined, with an analysis of angles and proportionality of sides. Suitable for students in Grades 9-10.

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