Step-by-step explanation:
Given:
∠2 and ∠4 are the vertical angles
To prove:
∠2 ≅ ∠4
Solution:
        Statements                      Reasons
1). ∠2 and ∠4 are the vertical angles    1). Given
2). Lines m and n intersect at P. Â Â Â Â Â Â 2). Definition of vertical angles
2). ∠2 and ∠3 are the linear pairs      2). Given in the diagram
3). ∠2 + ∠3 = 180°                   3). Linear pair theorem
4). ∠3 and ∠4 are the linear pairs      2). Given in the diagram
5). ∠3 + ∠4 = 180°                   5). Linear pair theorem
6). ∠2 + ∠3 = ∠3 + ∠4               6). Transitive Property
7). ∠2 ≅ ∠4                        7). Subtraction property