Question

1. State whether each pair of lines are (a) parallel or (b) not parallel. Give reasons.
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Answer 1

parallel lines ==>

a) if a transversal intersects two lines such that the pair of alternate interior angles are equal, then the lines are parallel.

b) if a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.

100 + 80 = 180

f) if a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel.

lines that are not parallel ==>

c)  if a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.

100 + 75 ≠180

e) corresponding angles are not equal so the lines are not parallel.

g) opposite angles are not equal.

hope it helps !!

Answer 2

Step-by-step explanation:

parallel lines ==>

a) if a transversal intersects two lines such that the pair of alternate interior angles are equal, then the lines are parallel.

b) if a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.

100 + 80 = 180

f) if a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel.

lines that are not parallel ==>

c) if a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.

100 + 75 is not equal to180

e) corresponding angles are not equal so the lines are not parallel.

g) opposite angles are not equal.