Prove that the straight lines perpendicular to the same straight line are parallel to one another.

Question

Philoid · Accepted Answer

Let AB and CD perpendicular to the line MN

∠ABD = 90^o(Since, AB perpendicular MN) (i)

∠CON = 90^o(Since, CD perpendicular MN) (ii)

Now,

∠ABD = ∠CON = 90^o

Therefore,

AB ‖ CD (Since, corresponding angles are equal)