Question

parallel lines and their angles: theorems (p→q) and their converse (q→p)
corresponding angles theorem:
if two parallel lines are cut by a transversal, then
the corresponding angles are congruent.
corresponding angles converse
if two lines are cut by a transversal so the corresponding angles
are congruent, then the lines are parallel.
alternate interior angles theorem:
if two parallel lines are cut by a transversal, then
the alternate interior angles are congruent.
alternate interior angles converse
if two lines are cut by a transversal so the alternate interior angles
are congruent, then the lines are parallel.
alternate exterior angles theorem:
if two parallel lines are cut by a transversal, then
the alternate interior angles are congruent.
alternate exterior angles converse
if two lines are cut by a transversal so the alternate exterior angles are
congruent, then the lines are parallel.
consecutive interior angles theorem:
if two parallel lines are cut by a transversal, then
the consecutive interior angles are supplementary.
consecutive interior angles converse
if two lines are cut by a transversal so the consecutive interior angles are
supplementary, then the lines are parallel.
transitive property of parallel lines
if two lines are parallel to the same line, then they are parallel to each other.

1. select all that apply:

this diagram represents which of the
following theorems ...
corresponding angles theorem
consecutive interior angles
theorem
alternative exterior angles
theorem
alternate interior angles theorem

Explanation:

• Corresponding Angles Theorem: States that if two parallel lines are cut by a transversal, then corresponding angles are congruent. In the diagram (assuming the standard parallel - transversal setup), if the lines are parallel and we have angles in corresponding positions (e.g., angle 2 and angle 6 in a typical parallel - transversal figure), this theorem applies.
• Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary. In a parallel - transversal configuration, consecutive interior angles (e.g., angles that lie between the two parallel lines and on the same side of the transversal) sum up to \(180^{\circ}\).
• Alternate Exterior Angles Theorem: When two parallel lines are cut by a transversal, alternate exterior angles (angles outside the two parallel lines and on opposite sides of the transversal) are congruent.
• Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, alternate interior angles (angles between the two parallel lines and on opposite sides of the transversal) are congruent.

Answer:

Corresponding Angles Theorem, Consecutive Interior Angles Theorem, Alternate Exterior Angles Theorem, Alternate Interior Angles Theorem