Question

examine whether lines perpendicular to the same line are parallel to each other
please answer fast

Answer 1

Given :   lines perpendicular to the same line are parallel to each other

To Find : True or False

Solution:

lines perpendicular to the same line are parallel to each other  is TRUE.

Proof

Let say  a line   l1 with slope  m

and there are two lines  l2  and l3   perpendicular to l1

and slope of l2 and l3  are  m2 and  m3 respectively.

Now : Use two facts :

Product of slopes of line perpendicular to each other is - 1 .

Line having same slope are parallel

lines  l2  perpendicular to lines  l1

=> (m2) * m = - 1

=> m2  = - 1/m

lines  l3  perpendicular to lines  l1

=> (m3) * m = - 1

=> m3  = - 1/m

Hence  m2  = m3  = - 1/m

As slope of l2 and l3 are same

Hence lines l2 and l3 are parallel to each other

Learn More:

7. If a transversal intersects two lines parallel lines then prove that ...

brainly.in/question/18440350

If ABC and PQR are two parallel line, then prove that the bisector of ...

brainly.in/question/13868130

In a given figure,AP is bisector of angle a and CQ is the bisector of ...

brainly.in/question/12889732