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. 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