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Which postulate or theorem can be used to prove the triangles congruent?

To determine which postulate or theorem can be used to prove the triangles congruent in the given image, let's analyze the triangles.

### Observations:
1. There are two right triangles.
2. They share a common angle, which is the one at the bottom left.
3. The right angle in each triangle is clearly marked.
4. The triangles share a common side, which is the side connecting the two right angles.

### Conclusion:
Given that:
- Both triangles are right triangles (each has a right angle).
- They share a common side (one of the legs of the triangles).
- They share a common angle (the angle adjacent to the common side).

We can use the **Angle-Angle-Side (AAS) Congruence Theorem** to prove that the two triangles are congruent. The AAS Theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

**Would you like more details on this theorem, or do you have any other questions?** 

Here are 5 related questions you might consider:

1. What are the conditions for the Side-Angle-Side (SAS) Congruence Postulate?
2. How does the Hypotenuse-Leg (HL) Congruence Theorem differ from the AAS Theorem?
3. Can the Angle-Side-Angle (ASA) Congruence Postulate be applied to these triangles?
4. What are some real-world applications of triangle congruence?
5. How can you prove two triangles are similar rather than congruent?

**Tip:** When proving triangle congruence, always look for shared angles or sides first; they often simplify the process.

Learn how to prove triangles congruent using the Angle-Angle-Side (AAS) Congruence Theorem with a step-by-step explanation. Understand the conditions required and examples of applying this theorem in geometric problems. Suitable for high school students.

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