In this chapter we will prove that the perpendicular line is the shortest distance between a point and a line.

**Given:**

Given above is the line L and point P.

The distance between point P and line L is shown by two segment PM and PR.

PM is the perpendicular segment which intersect line L at 90 degree angle.

**To prove:**

The shortest distance between point P and line M is shown by perpendicular line PM.

**Proof:**

Consider triangle PMR.**∠PMR = 90 degree** (as PM is perpendicular line )

We know that in a triangle, **if one of the angle is right angle ( 90 degree ) then the other two angle would definitely be acute angle.**

This means that the other two angles are less than ∠PMR .

**∠PRM < ∠PMR **

In a triangle,** the side opposite to larger angle is greater**.

Hence, side PM < PR.

So we proved that perpendicular line PM is the shorter side.