Question

paragraph proof: if two lines are perpendicular to the same line, then they are parallel to each other. diagram below. please help, ill fan

Answer 1

We are given that line r is perpendicular to line s, and line t is perpendicular to line s. Angles 1,2,3, and 4 are 90 degrees since line r is perpendicular to line s. Angles 5,6,7,and 8 are 90 degrees since line t is perpendicular to line s. Line s is a transversal since it crosses lines r and t at different points. Since lines r and t are cut by transversal line s and each pair of alternate interior angles is congruent, then lines r and t are parallel.

Answer 2

so basically its all the reasons put together?

Answer 3

You are using postulates, defined to be true but not proven to be true, and theorems, already proven to be true, that you already know or have covered in class to prove something else to be true.

So yes, all these postulates and theorems when put together allow you to prove something else is true.