Given:
∠2 and ∠4 are vertical angles
Prove
∠2 ≅ ∠4
1. ∠2 and ∠4 are vertical angles (given)
2. ∠2 and ∠3 are linear pair (definition of a linear pair)
3. m∠2 + m∠3 = 180° (angle addition postulate)
4. ∠3 and ∠4 are linear pair (definition of linear pair)
5. m∠3 + m∠4 = 180° (angle addition postulate)
6. m∠2 + m∠3 = m∠3 + m∠4 (substitution property) *substituted from 180°*
7. m∠2 = m∠4 (subtraction property) *subtracted m∠3 from both sides*
8. ∠2 ≅ ∠4 (definition of congruent angles)
