Question

which types of angles are congruent to each other? (choose as many as you feel are correct)
vertical angles
linear pair
alternate interior
alternate exterior
corresponding
consecutive interior
consecutive exterior

Explanation:

• Vertical angles: By the vertical - angles theorem, vertical angles (opposite angles formed by two intersecting lines) are congruent.
• Alternate interior angles: When two parallel lines are cut by a transversal, alternate interior angles are congruent (by the alternate - interior - angles theorem).
• Alternate exterior angles: When two parallel lines are cut by a transversal, alternate exterior angles are congruent (by the alternate - exterior - angles theorem).
• Corresponding angles: When two parallel lines are cut by a transversal, corresponding angles are congruent (by the corresponding - angles postulate).

A linear pair of angles is supplementary (\(m\angle1 + m\angle2=180^{\circ}\)), not necessarily congruent. Consecutive interior angles (also called same - side interior angles) are supplementary (\(m\angle1 + m\angle2 = 180^{\circ}\)) when two parallel lines are cut by a transversal, not congruent. Consecutive exterior angles (also called same - side exterior angles) are supplementary (\(m\angle1 + m\angle2=180^{\circ}\)) when two parallel lines are cut by a transversal, not congruent.

Answer:

vertical angles, alternate interior, alternate exterior, corresponding