Question

given
∠1 and ∠2 form a linear pair
∠1 ≅ ∠2
∠3 is a right angle
prove
∠1 ≅ ∠3
statement

1. ∠1 and ∠2 form a linear pair
2. ∠1 and ∠2 are supplementary
3. ∠1 ≅ ∠2
4. ∠1 is a right angle
5. ∠3 is a right angle
6. ∠1 ≅ ∠3

reason

1. given
2. definition of a

linear pair

1. given
2. supplementary

right angles
theorem

1. given
2. ?

what geometric reason justifies the transition from
statement 4 and 5 to statement 6?
supplementary right angles theorem
vertical angles theorem
congruent right angles theorem
congruent complements theorem

Explanation:

Step1: Analyze Statement 4 and 5

Statement 4: \( \angle1 \) is a right angle. Statement 5: \( \angle3 \) is a right angle.

Step2: Apply Congruent Right Angles Theorem

The Congruent Right Angles Theorem states that all right angles are congruent. Since \( \angle1 \) and \( \angle3 \) are both right angles (from statements 4 and 5), we can conclude \( \angle1\cong\angle3 \).

Answer:

Congruent Right Angles Theorem