Question:
Prove that the straight lines perpendicular to the same straight line are parallel to one another.
Solution:
Let AB and CD be drawn perpendicular to the Line MN
∠ABD = 90° [AB is perpendicular to MN] .... (i)
∠CON = 90° [CD is perpendicular to MN ] .... (ii)
Now,
∠ABD = ∠CDN = 90° [From (i) and (ii)]
Therefore, AB ∥CD, Since corresponding angles are equal.