Question

For problems 6-9, determine which lines, if any, can be proven parallel using the given information andfind the transversal that cuts the parallel lines. Justify your answer using an angle pair converse.6. 41 345m7. 43 413137614/1597210/118. 41 411P9. 416 and 49 are supplementary

Answer 1

We are given two pairs of lines. In the given diagram we have the following relationship between angles:

`\measuredangle1\cong\measuredangle5`

Angle 2 and angle 5 are corresponding angles and according to the Converse of the Corresponding Angles Theorem if two corresponding angles are congruent then the lines associated with these angles are parallel. In this case, lines "j" and "k" are parallel and the transversal line is "m". A similar procedure can be used with the other exercises having into account the angles that are congruent or the relationship given between them.