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.

One correct answer is:

Let m and n be lines that intersect line a. Let m be perpendicular to a. This means that all 4 of the angles formed by the intersection of m and a are 90°.

Let n be perpendicular to a. This means that all 4 of the angles formed by the intersection of n and a are also 90°.

Since all of the angles are congruent, this means that the same-side interior angles (between lines m and n) are congruent. If two same-side interior angles are congruent, then the lines are parallel.