Question

given: e || f and g is a transversal
prove: ∠1 ≅ ∠8
given that e || f and g is a transversal, we know that ∠4 ≅ ∠5 by the
alternate interior angles theorem. we also know that ∠1 ≅ ∠4 and
∠5 ≅ ∠8 by the _. therefore, ∠1 ≅ ∠8 by the substitution
property.
corresponding angles theorem
alternate exterior angles theorem
alternate interior angles theorem
vertical angles theorem

Explanation:

Vertical angles are formed when two lines intersect. In the given diagram, ∠1 and ∠4 are vertical angles (they are opposite each other at the intersection of lines \(e\) and \(g\)). Similarly, ∠5 and ∠8 are vertical angles (opposite each other at the intersection of lines \(f\) and \(g\)). The vertical angles theorem states that vertical angles are congruent.

Answer:

vertical angles theorem