Question

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.Given: rls, tisProve: r(4 points)

Answer 1

Explanation:

• Two lines are ,perpendicular, if the product of their slopes is -1.

,

• Two lines are ,parallel, if they have the same slope.

Given that lines r and t are perpendicular to line s. Let the slope of line s be m.

Then, by the condition for perpendicularity:

• The slope of line r = -1/m

,

• The slope of line t = -1/m

Since r and t have the same slope, they are parallel to each other.