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.

Question

Mathematics

Peterson

27 June, 01:03

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.

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Answers (2)

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Gilmore · Answer 1

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.

Reyna Gay · Answer 2

Since r and t are each perpendicular to s, angles 1 and 5 are right angles and therefore are congruent corresponding angles. Since two lines cut by a transversal are parallel if the corresponding angles are congruent, lines r and t are parallel.