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The question is asking whether the two triangles shown are congruent, based on the given information.

Both triangles are right triangles with the following features:
- They each have a right angle (90°).
- They each have a 45° angle.
- They both have a side of length 12.

Since both triangles have two congruent angles (45° and 90°) and a congruent side (12), we can use the **AAS (Angle-Angle-Side)** theorem to prove that they are congruent.

The **AAS theorem** states that two triangles are congruent if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of the other triangle.

Thus, the triangles must be congruent. Therefore, the correct answer is **A. True**.

Would you like further details or have any questions?

Here are five related questions to expand on this concept:
1. How does the AAS theorem differ from the ASA theorem?
2. Can two triangles be congruent if they only have two congruent angles?
3. How does the SSS (Side-Side-Side) theorem establish congruence between triangles?
4. What are some real-life applications of triangle congruence in engineering or architecture?
5. Why is it important for corresponding parts of congruent triangles to be congruent?

**Tip:** Always identify which sides or angles are involved before applying a congruence theorem, such as AAS or SSS.

The triangles shown below must be congruent. Is this true or false?

This question explores triangle congruence using the AAS (Angle-Angle-Side) theorem. Two right-angled triangles with congruent angles and sides are compared to determine if they are congruent. Suitable for students in Grades 8-10.

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