Question

Determine which lines, if any, must be parallel. If any lines are parallel, explain your reasoning using if-then statements or the name of the property used.
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Answer 1

Answer:

  a. a║b

  b. c║d

  c. AB║CD

  d. none

Step-by-step explanation:

a. If distinct lines in a plane are perpendicular to the same line, then they are parallel.

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b. If same-side interior angles are supplementary where a transversal crosses two lines in the same plane, then those two lines are parallel.

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c. If alternate interior angles are congruent where a transversal crosses two lines in the same plane, then those two lines are parallel. (Here, the measure of the upper angle at A is 180°-78°-67° = 35°, congruent with the lower angle at C. Those two angles are alternate interior angles with respect to lines AB and CD and transversal AC.)

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d. The marked angles are unrelated to each other, so define nothing about the relationship between lines a and b, or between lines c and d. However, they do mean that if a║b, then c║d.