Question

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.

$\bigcirc$ corresponding angles theorem
$\bigcirc$ alternate interior angles theorem
$\bigcirc$ vertical angles theorem
$\bigcirc$ alternate exterior angles theorem

Explanation:

$\angle1$ and $\angle4$ are opposite (vertical) angles formed by intersecting lines $e$ and $g$. $\angle5$ and $\angle8$ are opposite (vertical) angles formed by intersecting lines $f$ and $g$. The vertical angles theorem states that such opposite angles are congruent. This matches the missing justification in the proof.

Answer:

vertical angles theorem