Question 2 of 10 If two triangles are congruent, which of the following statements must be true? Check all that apply. $$ \square $$ A. The corresponding sides of the triangles are congruent. $$ \square $$ B. The triangles have the same size. $$ \square $$ C. The corresponding angles of the triangles are congruent. $$ \square $$ D. The triangles have the same shape.

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UpStudy AI · Accepted Answer

Below is the step-by-step reasoning:

1. **Understanding Congruency:**

Two triangles are said to be congruent if all their corresponding sides and angles are equal. This means that every side of one triangle is equal to its corresponding side in the other triangle, and every angle of one triangle is equal to its corresponding angle in the other triangle.

2. **Evaluating the Statements:**

- **Statement A:**  
     *The corresponding sides of the triangles are congruent.*  
     Since congruent triangles have all corresponding sides equal, this statement is **true**.

- **Statement B:**  
     *The triangles have the same size.*  
     Congruency ensures that the triangles have exactly the same dimensions, meaning they are the same size. This statement is **true**.

- **Statement C:**  
     *The corresponding angles of the triangles are congruent.*  
     In congruent triangles, each angle in one triangle is equal to the corresponding angle in the other triangle. Therefore, this statement is **true**.

- **Statement D:**  
     *The triangles have the same shape.*  
     Since congruent triangles have exactly the same side lengths and angles, they are identical in shape. Thus, this statement is **true**.

3. **Conclusion:**

All the statements (A, B, C, and D) are correct because they are all properties of congruent triangles.

**Final Answer:**  
$$ \boxed{A, B, C, 	ext{ and } D} $$
All four statements A, B, C, and D are true for congruent triangles.

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