The two triangles shown in the image have corresponding congruent angles and sides marked. To determine whether the two triangles can be proven congruent, we will evaluate the relationships between the sides and angles based on congruence postulates.

Analysis:

1. Angle-Angle-Side (AAS) Postulate:
   • The first triangle has two angles marked as congruent to corresponding angles in the second triangle.
   • Additionally, a non-included side is marked as congruent between the two triangles.
   • This satisfies the AAS Congruence Postulate, which states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Conclusion:

The two triangles can be proven congruent by the AAS Congruence Postulate.

Would you like more detailed reasoning or explanation on this? Here are 5 related questions and a tip to deepen your understanding:

1. How does the AAS postulate differ from the ASA postulate in proving triangle congruence?
2. Can congruence be established if the given side were included between the two angles?
3. Why is it important to check for all marked correspondences between sides and angles?
4. Could these triangles also be congruent using another postulate or theorem?
5. How do congruent triangles affect the properties of other geometric figures, like quadrilaterals or polygons?

Tip: Always verify the labeling of angles and sides carefully when using congruence postulates to avoid mismatched correspondences.