if two lines are perpendicular to the same line, prove the two lines are parallel to each other

Question

mathslover · Answer

yes.. So let us draw a diagram first. |dw:1363873135941:dw|

mathslover · Answer

We have two lines "l" and "m" .. which are perpendicular to the same line.

Can you notice the two right angles there?

anonymous · Answer

yeah

mathslover · Answer

What type of angles they are?

mathslover · Answer

Corresponding angles / alternate angles .. or veritcally opposite ones?

anonymous · Answer

i wanna say corresponding?

mathslover · Answer

yes! Those angles are corresponding angles but they are also equal ( = 90 degrees) 

hence the two lines are parallel .. Why? Because if the corresponding angles are equal then the two lines are parallel

directrix · Answer

"if two lines are perpendicular to the same line, prove the two lines are parallel to each other" should read as follows:

In a plane, if two lines are perpendicular to the same line, they are parallel to each other. Otherwise, the possibility exists that the two lines perpendicular to the same line are skew to each other.