Question

s cut by a transversal
given ( e parallel f ) and ( g ) is a transversal
prove: ( angle 1 cong angle 8 )
given that ( e parallel f ) and ( g ) is a transversal, we know that ( angle 4 cong angle 5 ) by the
alternate interior angles theorem. we also know that ( angle 1 cong angle 4 ) and ( angle 5 cong angle 8 )
by the ________. therefore, ( angle 1 cong angle 8 ) by the substitution property
vertical angles theorem
alternate interior angles theorem
alternate exterior angles theorem
corresponding angles theorem

Explanation:

Vertical angles are formed when two lines intersect. In the given diagram, \(\angle1\) and \(\angle4\) are vertical angles, and \(\angle5\) and \(\angle8\) are vertical angles. The vertical angles theorem states that vertical angles are congruent. Since we know \(\angle1\cong\angle4\) and \(\angle5\cong\angle8\) (by the property of vertical angles), and \(\angle4\cong\angle5\) (alternate interior angles theorem for parallel lines \(e\parallel f\) and transversal \(g\)), we can use substitution to get \(\angle1\cong\angle8\).

Answer:

vertical angles theorem