The two triangles in the image, $\triangle RQS$ and $\triangle VUT$, are similar based on angle-angle (AA) similarity. They have corresponding angles of 76°, 76°, and 28°, which are equal in both triangles. This information allows us to set up a similarity statement by matching the vertices of each triangle in corresponding order.

The similarity statement for these triangles would be: $\triangle RQS \sim \triangle VUT$

Here, each vertex corresponds to the angle in each triangle as follows:

• $R$ (28°) corresponds to $V$ (28°),
• $Q$ (76°) corresponds to $U$ (76°), and
• $S$ (76°) corresponds to $T$ (76°).

Would you like a deeper explanation, or do you have any other questions?

Related Questions:

1. How can we use side ratios to verify the similarity between two triangles?
2. What are the different criteria for proving triangle similarity (e.g., AA, SSS, SAS)?
3. How would we calculate the missing side lengths if the triangles were similar with known scale factors?
4. Can two triangles be similar if only two angles are known to be equal?
5. What is the significance of corresponding angles in similar triangles?

Tip:

When proving similarity, always identify the corresponding angles and sides clearly to set up a correct similarity statement.