**Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.**

**Solution:**

Let's suppose that we have line . A is any point from where we draw perpendicular AB to line . Suppose there is any other random point C present on the line . Join A and C.

So, we have right angled at B.

We need to prove that AB is shorter than AC.

** (AB is perpendicular to line ) (1)**

** (Angle sum property of triangle)**

Putting **(1)** in the above equation, we get

and

It means that is the largest angle in .

Therefore,

**(In any triangle, the side opposite to the larger angle is longer.)**

Similarly, we can choose any random point present on line and can complete a triangle in the same way. AB would be shortest of all the line segments. We can prove this using the same method.