The image shows two triangles, and we are tasked with determining whether they are congruent. Additionally, we are to identify the postulate or theorem that justifies the congruence if they are indeed congruent.

Step 1: Identifying Key Features

From the image:

• Both triangles share a vertical angle (the top angle).
• One pair of corresponding sides is marked as congruent (the side with the tick marks).
• A pair of corresponding angles is also marked as congruent.

Step 2: Congruence Postulate

The triangles have two angles and one included side that are congruent. This situation matches the ASA Postulate (Angle-Side-Angle). According to the ASA postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

Conclusion

The two triangles are congruent by the ASA Postulate.

Do you want more details or have any questions about this?

Here are 5 related questions for further exploration:

1. What are the other congruence postulates besides ASA?
2. How does the ASA Postulate differ from the AAS Theorem?
3. Can triangles be congruent by only knowing that two sides are congruent?
4. What is the significance of the included side in the ASA Postulate?
5. What is a real-life application of triangle congruence?

Tip: Always check if corresponding angles and sides match in any triangle congruence problem!