Question

1. (l27) given: ∠2 and ∠7 are supplementary prove: m || n 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. 20. (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 angles form a linear pair, then they are supplementary.

Explanation:

Step1: Recall angle - pair relationships in parallel lines

When two parallel lines are cut by a transversal, different angle - pair relationships exist. Supplementary angles add up to 180 degrees.

Step2: Analyze the given information in problem 19

Given that \(m\parallel n\) and \(\angle2\) and \(\angle7\) are supplementary. We know that when two parallel lines are cut by a transversal, same - side interior angles are supplementary.

Step3: Analyze the given information in problem 20

Given that lines \(m\) and \(t\) intersect and \(\angle3\) and \(\angle4\) are supplementary. By the definition of a linear pair, if two angles form a linear pair, they are supplementary.

Answer:

1. Given two parallel lines \(m\parallel n\), \(\angle2\) and \(\angle7\) are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary.
2. Since \(\angle3\) and \(\angle4\) are formed by the intersection of lines \(m\) and \(t\) and are supplementary, by the definition of a linear pair (if two angles form a linear pair, then they are supplementary), the reason is the definition of a linear pair.