Question

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

1. ∠1 and ∠2 form a linear pair
2. ∠1 and ∠2 are supplementary
3. ∠3 is vertical to ∠1
4. ∠1 ≅ ∠3
5. ∠2 ≅ ∠3
6. ∠1 ≅ ∠2
7. ∠1 is a right angle

reason

1. given
2. definition of a linear pair
3. given
4. ?
5. given
6. transitive property
7. supplementary right angles theorem

what geometric reason justifies the transition from
statement 3 to statement 4?

Explanation:

Vertical Angles Theorem states that if two angles are vertical angles, then they are congruent. In this case, statement 3 says ∠3 is vertical to ∠1 (given), and statement 4 is ∠1 ≅ ∠3. The Vertical Angles Theorem directly justifies that vertical angles (∠1 and ∠3 here) are congruent.

Answer:

Vertical Angles Theorem