https://file.aiquickdraw.com/mathbot/file/17263487615470e4e4g91.jpg

The problem involves proving the theorem: "All right angles are congruent." Here's a detailed explanation of how to complete the proof based on the given image.

### Given Information
- **Given:** ∠A and ∠B are right angles.
- **Prove:** ∠A ≅ ∠B.

### Proof Structure
The proof uses a two-column format with **Statements** and **Reasons**.

1. **Statement 1:** ∠A and ∠B are right angles.
   - **Reason 1:** Given.

2. **Statement 2:** \( m\angle A = 90^\circ \) and \( m\angle B = 90^\circ \).
   - **Reason 2:** Definition of right angles (A right angle is defined as an angle that measures 90 degrees).

3. **Statement 3:** \( m\angle A = m\angle B \).
   - **Reason 3:** Substitution property (Both angles have been shown to measure 90 degrees, so their measures are equal).

4. **Statement 4:** ∠A ≅ ∠B.
   - **Reason 4:** Definition of congruent angles (Two angles are congruent if they have the same measure).

### Completed Proof
Now that we've filled in the missing statements and reasons, the proof is logically sound and complete. It shows that since both angles are 90 degrees, they are equal in measure and therefore congruent.

Would you like further details or have any questions?

### 5 Related Questions to Explore
1. What is the definition of a right angle?
2. Can two angles be congruent if their measures are not equal?
3. What properties do congruent angles share?
4. How do the properties of equality apply to angle measures in proofs?
5. What other theorems rely on the concept that all right angles are congruent?

### Tip
Always start your geometric proofs by listing the given information and defining any necessary terms or properties before proceeding to further logical steps.

Prove that all right angles are congruent.

Explore the theorem that all right angles are congruent, including a step-by-step proof showing how right angles, defined as measuring 90 degrees, are always congruent. Suitable for students in Grades 8-10 studying basic geometry concepts.

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