7. Write a paragraph proof of theorem 3-8: in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Step-by-step explanation:

Assume that two lines x and y are perpendicular to the line z.

+) x intersects z at point A => Angle A1 = 90°

+) y intersects z at point B => Angle B1 = 90°

As it can be seen from the figure that Angle A1 and Angle B1 are corresponding angles and they are congruent.

According to the corresponding angle theorem, when two parallel lines are cut by a transversal, the pair of corresponding angles are congruent and vice versa, when two lines are cut by the same line and the pair of corresponding angles are congruent, they are parallel.

=> x and y are parallel.