To determine which similarity postulate or theorem proves that triangles Δ QRS and Δ TUV are similar, let's analyze the given information step-by-step:
1. Angle Information:
- In triangle Δ QRS, m∠ S = 73°.
- In triangle Δ TUV, m∠ V = 73°.
2. Similar Angle:
Both triangles Δ QRS and Δ TUV have an angle measuring 73°. Since both angles m∠ S in Δ QRS and m∠ V in Δ TUV are equal to 73°, we need to use this information along with other properties of the triangles.
3. Triangle Property:
Both given angles are within right triangles (right triangle Δ QRS and right triangle Δ TUV).
4. AA (Angle-Angle) Postulate:
According to the Angle-Angle (AA) similarity postulate, two triangles are similar if they have two corresponding angles that are congruent. Since both triangles include a right angle (90°) and they share another corresponding angle of 73°, the third angle in both triangles must also be equal, due to the angle sum property of triangles (sum of angles in a triangle is 180°).
Therefore, since both triangles share two corresponding congruent angles, they are similar by the AA (Angle-Angle) similarity postulate.
Conclusion:
The similarity postulate that proves Δ QRS and Δ TUV are similar is:
B. AA
