Question

Given: e parallel f and g is a transversal
Prove: Angle 1 Is-congruent-to Angle 8

Horizontal and parallel lines e and f are cut by transversal g. On line e where it intersects line g, 4 angles are formed. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line f where it intersects line g, 4 angles are formed. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7.

Given that e parallel f and g is a transversal, we know that Angle 4 Is-congruent-to Angle 5 by the alternate interior angles theorem. We also know that Angle 1 Is-congruent-to Angle 4 and Angle 5 Is-congruent-to Angle 8 by the ________. Therefore, Angle 1 Is-congruent-to Angle 8 by the substitution property.

corresponding angles theorem
alternate interior angles theorem
vertical angles theorem
alternate exterior angles theorem

Answer 1

vertical angles theorem