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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04-10-2016
Mathematics

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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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MsEHolt MsEHolt · Answer 1 · 2018-07-26T03:25:36+02:00

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.