Option A: >
Solution:
Given a triangle GHJ.
The line GH is perpendicular to line HJ.
This means the triangle is a right angled triangle.
In ΔGHJ, GH is the base of the triangle and
HJ is a height of the triangle.
Then the third side must be the hypotenuse of the right triangle.
We know that by the Pythagoras theorem,
[tex](\text {Hypotenuse})^2=(\text{Base})^2+(\text{Height})^2[/tex]
[tex](\text {GJ})^2=(\text {GH})^2+(\text {HJ})^2[/tex]
This clearly shows that the hypotenuse is greater than the height.
⇒ GJ > HJ
Option A: > is the correct answer.
If line GH is perpendicular to line HJ, then GJ is > HJ.
