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:

Step1: Analyze question 20

We know that when two lines intersect, the adjacent - angles formed are linear pairs. By the property that if two angles form a linear pair, then they are supplementary.

Step2: Analyze question 21

It is a well - known parallel - line postulate that if two lines form congruent corresponding angles with a transversal, then the lines are always parallel.

Step3: Analyze question 22

By the definition of parallel lines, two parallel lines never intersect.

Answer:

1. E. If two angles form a linear pair, then they are supplementary.
2. A. always
3. C. never