Question

a. definition of parallel lines
b. if two lines form congruent alternate interior angles with a transversal, then the lines are parallel.
c. if two lines form congruent corresponding angles, then the lines are parallel.
d. if two lines form supplementary interior angles on the same side of a transversal, then the lines are parallel.
e. if two lines form congruent alternate exterior angles, then the lines are parallel.

1. (l17) given: lines m and t intersect prove: ∠3 and ∠4 are supplementary

a. definition of supplementary angles
b. vertical angles are congruent.
c. if two parallel lines are cut by a transversal, then interior angles on the same side of the transversal are supplementary.
d. definition of a linear pair
e. if two angles form a linear pair, then they are supplementary.

1. (l27) if two lines form congruent corresponding angles with a transversal, then the lines are ______ parallel.

a. always
b. sometimes
c. never
d. definitely
e. none of the above

1. (l22) if two lines are parallel, then they ______ intersect.

a. always
b. sometimes
c. never
d. definitely
e. none of the above

1. determine all the missing steps in the proof below, then identify which partial set of missing steps is correct.

given: (overline{ma}perpoverline{pa}); (angle mpa) is complementary to (angle ram) prove: (mpparallel rn)

Explanation:

• Question 20: When two lines intersect, the adjacent angles formed are a linear - pair. By the definition, if two angles form a linear pair, they are supplementary. So, ∠3 and ∠4 are supplementary because they form a linear pair.
• Question 21: One of the well - known parallel line postulates is that if two lines form congruent corresponding angles with a transversal, then the lines are always parallel.
• Question 22: Parallel lines are defined as lines in the same plane that do not intersect. So, if two lines are parallel, they never intersect.

Answer:

• 20. E. If two angles form a linear pair, then they are supplementary.
• 21. A. always
• 22. C. never