Question

hello i am clueless! http://prntscr.com/cyxrov

Answer 1

@pooja195

Answer 2

@mathmale

Answer 3

@Nnesha @zepdrix @Loser66 please help me :P

Answer 4

Now, suppose r is not parallel to t

Answer 5

then, r and t intersect at somewhere. Without Loss of Generality, assume they intersect from the Left at A , we have A B C is a right triangle.

Answer 6

Since r \(\perp\)s, so \(\angle ABC = 90^0\)

Answer 7

that gives us \(\angle ACB < 90\)
That contradicts to the given information, which says \(t\perp s\)

Hence r // t

Answer 8

okay

Answer 9

um

Answer 10

well i know that they are parallel if they are perpendicular to the same line, i just dont know how to write a paragraph proof @loser66

Answer 11

just write as what I did here.

Answer 12

okay thanks, do i need to mention other theorems? @Loser66

Answer 13

Nope.

Answer 14

That was an indirect proof.

Here is a direct proof.

We are given that \(r \perp s\) and \(t \perp s\). That makes angles 2 and 6 right angles by the definition of peprpendicular lines. Angles 2 and 6 are congruent by the theorem that states that all right angles are congruent. We then conclude that \(r \parallel t\) by the postulate that states that if two lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel.

Answer 15

rip my grade