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The problem presents a parallelogram \(ABCD\) with the following conditions:
- \(\angle ABC\) is a right angle.
- Diagonals \(AC \cong BD\) (they are congruent).

Let's analyze the questions.

### 1. **Can the parallelogram be a square?**
For a parallelogram to be a square, the following conditions must hold:
- All angles must be right angles.
- All sides must be congruent (equal in length).
- The diagonals must be congruent.

Since we know that \(\angle ABC\) is a right angle and that the diagonals \(AC \cong BD\), the parallelogram might be a rectangle. However, to determine if it must be a square, we'd also need to check if all the sides are congruent. 

Without explicit information about the sides of the parallelogram, we can't definitively say that it *must* be a square. Therefore, **the answer would be "No"**—the parallelogram is not necessarily a square.

### 2. **Supporting Theorems** 
The two theorems you need to match with the properties given are:
1. **Parallelogram \(ABCD\) is a rectangle:** The fact that one angle is a right angle and the diagonals are congruent guarantees that the parallelogram is a rectangle. This follows from the **Rectangle Diagonal Theorem**, which states that if the diagonals of a parallelogram are congruent and one angle is a right angle, the parallelogram is a rectangle.

2. **Diagonals \(AC \cong BD\):** This property is given directly in the problem. The congruence of the diagonals is a characteristic of rectangles and squares but doesn't by itself prove the shape is a square.

Would you like more details on these theorems?

Given: ∠ABC is a right angle; AC ≅ BD. Must the parallelogram be a square? Choose the numbers of the theorems that support your answer.

Explore if a parallelogram with a right angle and congruent diagonals must be a square. Understand the properties of parallelograms, rectangles, and squares, and learn about the Rectangle Diagonal Theorem and other relevant theorems.

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