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what’s the congruence statement of these triangles? 1.AAS

In the image, there are two triangles that share a common angle, and other angles and sides seem to be marked to indicate congruence.

Given that you mentioned "AAS" (Angle-Angle-Side) as the congruence criterion, let's identify the congruent parts:

### AAS Congruence:
For two triangles to be congruent by the AAS criterion, two angles and the non-included side (the side that is not between the two angles) in one triangle must be congruent to the corresponding two angles and the non-included side in another triangle.

### Congruence Statement:
Let's denote the two triangles as \( \triangle ABC \) and \( \triangle DEF \). Based on AAS:
1. \( \angle A \cong \angle D \) (corresponding angles are congruent).
2. \( \angle B \cong \angle E \) (another pair of corresponding angles are congruent).
3. The side opposite to the congruent angles, say \( BC \) in \( \triangle ABC \) and \( EF \) in \( \triangle DEF \), are also congruent.

So the congruence statement would be:
\[ \triangle ABC \cong \triangle DEF \] by AAS.

Would you like more details or have any other questions?

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Here are 5 related questions you might explore:

1. How does the AAS criterion differ from ASA (Angle-Side-Angle) congruence?
2. Can you always determine the congruence of two triangles if two angles and a side are given?
3. What are the other criteria for triangle congruence?
4. How can you use triangle congruence to solve problems involving perimeter or area?
5. What are some real-world applications of triangle congruence?

**Tip:** Remember, in AAS congruence, it's important that the side is not between the two angles, differentiating it from ASA (Angle-Side-Angle) congruence, where the side must be between the two angles.

Explore the AAS (Angle-Angle-Side) criterion for triangle congruence. Learn how two triangles are congruent if two angles and the non-included side are congruent. Includes a detailed explanation and examples.

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