Question

given: e || f and g is a transversal
prove: ( angle 1 cong angle 8 )
given that e || 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.
corresponding angles theorem
alternate interior angles theorem
vertical angles theorem
alternate exterior angles theorem

Explanation:

Vertical angles are formed when two lines intersect. They are opposite each other and are congruent. In the given diagram, ∠1 and ∠4 are vertical angles (formed by the intersection of lines \(e\) and \(g\)), and ∠5 and ∠8 are vertical angles (formed by the intersection of lines \(f\) and \(g\)). The corresponding angles theorem relates angles in the same relative position when a transversal crosses parallel lines. The alternate - interior angles theorem relates angles between the parallel lines and on opposite sides of the transversal. The alternate - exterior angles theorem relates angles outside the parallel lines and on opposite sides of the transversal. Since ∠1 and ∠4, ∠5 and ∠8 are pairs of vertical angles, the vertical angles theorem is the correct one.

Answer:

vertical angles theorem